A376518 E.g.f. satisfies A(x) = exp(x^3 * (1 + x) * A(x)).
1, 0, 0, 6, 24, 0, 1080, 15120, 60480, 967680, 29030400, 319334400, 3772137600, 129729600000, 2724321600000, 41366099174400, 1238803517952000, 38414242234368000, 840907325318860800, 23606245443503923200, 878145842759657472000, 26509751796795531264000
Offset: 0
Links
- Eric Weisstein's World of Mathematics, Lambert W-Function.
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-x^3*(1+x))))) -
PARI
a(n) = n!*sum(k=0, n\3, (k+1)^(k-1)*binomial(k, n-3*k)/k!);
Formula
E.g.f.: exp( -LambertW(-x^3 * (1+x)) ).
a(n) = n! * Sum_{k=0..floor(n/3)} (k+1)^(k-1) * binomial(k,n-3*k)/k!.