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A369887
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Sum of products of squares of parts , counted without multiplicity, in all partitions of n.
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1
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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, 5166820832
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OFFSET
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0,3
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LINKS
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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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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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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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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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