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A308861
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Expansion of e.g.f. 1/(1 - x*(1 + x)*exp(x)).
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7
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1, 1, 6, 39, 352, 3965, 53556, 844123, 15204960, 308118105, 6937562980, 171826160231, 4642588564032, 135891789038629, 4283619809941668, 144674451274329075, 5211965027738046016, 199498704931954788785, 8085413817213212761668, 345895984008645703002559
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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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E.g.f.: 1 / (1 - Sum_{k>=1} k^2*x^k/k!).
a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * k^2 * a(n-k).
a(n) ~ n! / (r^(n+1) * exp(r) * (1 + 3*r + r^2)), where r = A201941 = 0.44413022882396659058546632949098466707932096994213775695918... is the root of the equation exp(r)*r*(1 + r) = 1. - Vaclav Kotesovec, Jun 29 2019
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MATHEMATICA
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nmax = 19; CoefficientList[Series[1/(1 - x (1 + x) Exp[x]), {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k] k^2 a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 19}]
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PROG
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(PARI) my(x='x+O('x^25)); Vec(serlaplace(1/(1 - x*(1 + x)*exp(x)))) \\ Michel Marcus, Mar 10 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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