A378016 E.g.f. satisfies A(x) = (1+x) * exp( x * (1+x)^2 * A(x) ).
1, 2, 11, 115, 1617, 30241, 701923, 19517975, 633387905, 23513238865, 983268873891, 45750603668815, 2344878934878769, 131285573039583977, 7973124098907905603, 522086636316439329511, 36669284618683152764289, 2750044026126526125774625, 219342360538110975815216323
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)*exp(-lambertw(-x*(1+x)^3)))) -
PARI
a(n) = n!*sum(k=0, n, (k+1)^(k-1)*binomial(3*k+1, n-k)/k!);
Formula
E.g.f.: (1+x) * exp( -LambertW(-x * (1+x)^3) ).
a(n) = n! * Sum_{k=0..n} (k+1)^(k-1) * binomial(3*k+1,n-k)/k!.