A378017 E.g.f. satisfies A(x) = (1+x)^2 * exp( x * (1+x) * A(x) ).
1, 3, 15, 148, 2077, 38326, 883369, 24431436, 789531705, 29213730010, 1218401262541, 56566561281616, 2893886178904549, 161768999193007974, 9811122121462081281, 641683497800057913556, 45022670799746182036465, 3373421864644139722767538, 268843153008388446079159573
Offset: 0
Keywords
Links
- Eric Weisstein's World of Mathematics, Lambert W-Function.
Programs
-
PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace((1+x)^2*exp(-lambertw(-x*(1+x)^3)))) -
PARI
a(n) = n!*sum(k=0, n, (k+1)^(k-1)*binomial(3*k+2, n-k)/k!);
Formula
E.g.f.: (1+x)^2 * exp( -LambertW(-x * (1+x)^3) ).
a(n) = n! * Sum_{k=0..n} (k+1)^(k-1) * binomial(3*k+2,n-k)/k!.