Revision History for A088312
(Underlined text is an addition;
strikethrough text is a deletion.)
Showing entries 1-10
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#36 by Peter Luschny at Wed Dec 14 06:30:08 EST 2022
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#35 by Peter Luschny at Wed Dec 14 06:26:52 EST 2022
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a(n) = (1/2)*(n-1)*n!*hypergeom([1 - n/2, 3/2 - n/2], [3/2, 3/2, 2], 1/4) for n >= 1. - Peter Luschny, Dec 14 2022
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| MAPLE
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A088312 := n -> ifelse(n=0, 1, (1/2)*(n - 1)*n!*hypergeom([1 - n/2, 3/2 - n/2], [3/2, 3/2, 2], 1/4)): seq(simplify(A088312(n)), n = 0..21); # Peter Luschny, Dec 14 2022
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approved
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#34 by Peter Luschny at Wed Dec 14 06:12:13 EST 2022
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#33 by Michel Marcus at Wed Dec 14 00:31:14 EST 2022
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#32 by G. C. Greubel at Wed Dec 14 00:01:15 EST 2022
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#31 by G. C. Greubel at Wed Dec 14 00:01:01 EST 2022
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| COMMENTS
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a(n) = (1/2)*(A000262(n) + (-1)^n*A111884(n)).
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a(n) = (1/2)*(A000262(n) + (-1)^n*A111884(n)). - Peter Bala, Mar 27 2022
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| MATHEMATICA
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Rest[Rest[With[{m=30}, CoefficientList[Series[Cosh[x/(1-x)], {x, , 0, 20, m}], x] * Range[0, 20]!]] (* _, m]!] (* _Vaclav Kotesovec_, Jul 04 2015 *)
Table[Sum[n!/(2*k)! Binomial[n - 1, 2*k - 1], {k, 0, Floor[n/2]}], {n, 0, 1230}] (* Emanuele Munarini, Sep 03 2017 *)
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| PROG
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(Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!(Laplace( Cosh(x/(1-x)) ))); // G. C. Greubel, Dec 13 2022
(SageMath)
def A088312_list(prec):
P.<x> = PowerSeriesRing(QQ, prec)
return P( cosh(x/(1-x)) ).egf_to_ogf().list()
A088312_list(40) # G. C. Greubel, Dec 13 2022
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| CROSSREFS
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Cf. A000262, A001710, A027187, A024429, A024430, A001710, A088313, A111884.
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approved
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#30 by Michel Marcus at Tue Mar 29 03:40:04 EDT 2022
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#29 by Joerg Arndt at Tue Mar 29 03:32:54 EDT 2022
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#28 by Michel Marcus at Mon Mar 28 00:46:54 EDT 2022
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#27 by Michel Marcus at Mon Mar 28 00:46:50 EDT 2022
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| LINKS
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N. Heninger, E. M. Rains and N. J. A. Sloane, <a href="httphttps://arXivarxiv.org/abs/math.NT/0509316">On the Integrality of n-th Roots of Generating Functions</a>, arXiv:math/0509316 [math.NT], 2005-2006; J. Combinatorial Theory, Series A, 113 (2006), 1732-1745.
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proposed
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