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A351763
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Expansion of e.g.f. 1/(1 - 3*x*exp(x)).
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3
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1, 3, 24, 279, 4332, 84075, 1958058, 53202387, 1652070696, 57713665779, 2240196853710, 95650311987483, 4455281606078988, 224815388384744859, 12216916158370619010, 711312392929267383075, 44176151714082889756368, 2915038701200389804440675
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OFFSET
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0,2
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LINKS
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FORMULA
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E.g.f.: 1/(1 - 3*x*exp(x)).
a(n) = n! * Sum_{k=0..n} 3^(n-k) * (n-k)^k/k!.
a(0) = 1 and a(n) = 3 * n * Sum_{k=0..n-1} binomial(n-1,k) * a(k) for n > 0.
a(n) ~ n! / ((1 + LambertW(1/3)) * LambertW(1/3)^n). - Vaclav Kotesovec, Feb 19 2022
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PROG
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(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-3*x*exp(x))))
(PARI) a(n) = n!*sum(k=0, n, 3^(n-k)*(n-k)^k/k!);
(PARI) a(n) = if(n==0, 1, 3*n*sum(k=0, n-1, binomial(n-1, k)*a(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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