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A346888
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Expansion of e.g.f. 1 / (1 - x^2 * exp(x) / 2).
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6
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1, 0, 1, 3, 12, 70, 465, 3591, 31948, 319068, 3539385, 43205635, 575312826, 8298867798, 128921967265, 2145837600375, 38097353658120, 718657756980376, 14354000800751313, 302625047150614179, 6716038666999745710, 156498725047355717250, 3820426102008414736761
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OFFSET
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0,4
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LINKS
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FORMULA
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a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * binomial(k,2) * a(n-k).
a(n) ~ n! / ((1 + LambertW(1/sqrt(2))) * 2^(n+1) * LambertW(1/sqrt(2))^n). - Vaclav Kotesovec, Aug 08 2021
a(n) = n! * Sum_{k=0..floor(n/2)} k^(n-2*k)/(2^k * (n-2*k)!). - Seiichi Manyama, May 13 2022
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MATHEMATICA
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nmax = 22; CoefficientList[Series[1/(1 - x^2 Exp[x]/2), {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k] Binomial[k, 2] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 22}]
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PROG
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(PARI) my(x='x+O('x^25)); Vec(serlaplace(1/(1-x^2*exp(x)/2))) \\ Michel Marcus, Aug 06 2021
(PARI) a(n) = n!*sum(k=0, n\2, k^(n-2*k)/(2^k*(n-2*k)!)); \\ Seiichi Manyama, May 13 2022
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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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