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| A212580
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Number of equivalence classes of S_n under transformations of positionally and numerically adjacent elements of the form abc <--> acb where a<b<c.
(history;
published version)
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#51 by Joerg Arndt at Wed Feb 21 06:16:51 EST 2024
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#50 by Seiichi Manyama at Wed Feb 21 05:38:33 EST 2024
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#49 by Seiichi Manyama at Wed Feb 21 05:38:29 EST 2024
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a(n) = Sum_{k=0..floor(n/3)} (-1)^k * (n-2*k)! * binomilabinomial(n-2*k,k). (End)
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| STATUS
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approved
editing
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#48 by Michael De Vlieger at Tue Feb 20 11:18:57 EST 2024
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#47 by Seiichi Manyama at Tue Feb 20 11:03:35 EST 2024
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#46 by Seiichi Manyama at Tue Feb 20 10:44:14 EST 2024
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a(n) = Sum_{k=0..floor(n/3)} (-1)^k * (n-2*k) ! * )! * binomila(n-2*k,k). (End)
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#45 by Seiichi Manyama at Tue Feb 20 10:27:36 EST 2024
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G.f.: Sum_{k>=0} k! * ! * ( x^k * (1-x^2)^) )^k.
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| PROG
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(PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, k!*!*(x^k*(1-x^2)^))^k)) \\ Seiichi Manyama, Feb 20 2024
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#44 by Seiichi Manyama at Tue Feb 20 09:54:11 EST 2024
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From Seiichi Manyama, Feb 20 2024: (Start)
G.f.: Sum_{k>=0} k! * x^k * (1-x^2)^k. - _Seiichi Manyama_, Feb 20 2024.
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#43 by Seiichi Manyama at Tue Feb 20 09:52:56 EST 2024
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a(n) = Sum_{k=0..floor(n/23)} (-1)^k * (n-2*k) ! * binomila(n-2*k,k). (End)
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#42 by Seiichi Manyama at Tue Feb 20 09:48:49 EST 2024
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a(n) = Sum_{k=0..floor(n/2)} (-1)^k * (n-2*k) ! * binomila(n-2*k,k). (End)
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