Revision History for A369887
(Underlined text is an addition;
strikethrough text is a deletion.)
Showing all changes.
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#9 by Michael De Vlieger at Sun Feb 04 09:00:41 EST 2024
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#8 by Seiichi Manyama at Sun Feb 04 08:59:56 EST 2024
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#7 by Seiichi Manyama at Sun Feb 04 08:54:17 EST 2024
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| DATA
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1, 1, 5, 14, 34, 995, 36208, 108537, 4491090, 12122812, 44995566, 1091412480, 4328626199, 10329653486, 306994112866, 867763229111, 2165484450800, 6627800885030, 168272271778190, 422032123319846, 1043974366624376, 28296741412354288, 63219475823674929, 180924137243485580, 412026694681441398, 10256452121149864634, 23140530512273431081, 55030272918503205344, 130803096050906757150, 2912950241211630802024, 7390118039282920280596, 16346254237385166820832
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#6 by Seiichi Manyama at Sun Feb 04 08:53:39 EST 2024
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| DATA
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1, 1, 5, 14, 349, 9536, 208108, 537449, 10901212, 28124499, 556610914, 1248043286, 26199103296, 53486306994, 112866867763, 2291112165484, 4508006627800, 88503016827227, 177819042203212, 3319846104397436, 6624376282967414, 12354288632194758, 236749291809241372, 434855804120266946, 8144139810256452121, 14986463423140530512, 27343108155030272918, 503205344130803096050, 906757150291295024121, 1630802024739011803928, 29202805961634625423738
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#5 by Seiichi Manyama at Sun Feb 04 08:52:59 EST 2024
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| PROG
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(PARI) my(N=40, x='x+O('x^N)); Vec(prod(k=1, N, 1+k^2*x^k/(1-x^k)))
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#4 by Seiichi Manyama at Sun Feb 04 08:49:00 EST 2024
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| EXAMPLE
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The partitions of 4 are 4, 3+1, 2+2, 2+1+1, 1+1+1+1. So a(4) = 16 + 9 + 4 + 4 + 1 = 34.
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#3 by Seiichi Manyama at Sun Feb 04 08:43:44 EST 2024
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#2 by Seiichi Manyama at Sun Feb 04 08:39:47 EST 2024
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| NAME
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allocatedSum of products of squares of parts , counted without multiplicity, in all forpartitions Seiichiof Manyaman.
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| DATA
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1, 1, 5, 14, 34, 95, 208, 537, 1090, 2812, 5566, 12480, 26199, 53486, 112866, 229111, 450800, 885030, 1778190, 3319846, 6624376, 12354288, 23674929, 43485580, 81441398, 149864634, 273431081, 503205344, 906757150, 1630802024, 2920280596
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| OFFSET
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0,3
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| FORMULA
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G.f.: Product_{k>=1} 1 + k^2*x^k/(1-x^k).
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| CROSSREFS
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Cf. A162506.
Cf. A077335.
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| KEYWORD
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allocated
nonn
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| AUTHOR
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Seiichi Manyama, Feb 04 2024
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| STATUS
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approved
editing
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#1 by Seiichi Manyama at Sun Feb 04 08:39:47 EST 2024
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| NAME
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allocated for Seiichi Manyama
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| KEYWORD
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allocated
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| STATUS
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approved
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