A376515 E.g.f. satisfies A(x) = exp(x^2 * A(x) / (1 - x)).
1, 0, 2, 6, 60, 480, 5880, 75600, 1197840, 20865600, 415074240, 9067766400, 218808596160, 5739600746880, 163303845344640, 4998933984844800, 164036362839148800, 5740920215225395200, 213551108122018867200, 8412438143909940940800, 349915152951011468620800
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^2/(1-x))))) -
PARI
a(n) = n!*sum(k=0, n\2, (k+1)^(k-1)*binomial(n-k-1, n-2*k)/k!);
Formula
E.g.f.: exp( -LambertW(-x^2 / (1-x)) ).
a(n) = n! * Sum_{k=0..floor(n/2)} (k+1)^(k-1) * binomial(n-k-1,n-2*k)/k!.
a(n) ~ exp(1) * sqrt(1 + 4*exp(1) - sqrt(1 + 4*exp(1))) * 2^(n - 1/2) * n^(n-1) / ((1 + 2*exp(1) - sqrt(1 + 4*exp(1))) * (-1 + sqrt(1 + 4*exp(1)))^(n-1)). - Vaclav Kotesovec, Sep 26 2024