A367790 E.g.f. satisfies A(x) = exp( x/(1-x)^4 * A(x) ).

1, 1, 11, 148, 2669, 62056, 1777927, 60692920, 2408692505, 109074596320, 5553702114731, 314208715035304, 19561795753879909, 1329317730339826384, 97924919301787209647, 7773978186375852940696, 661702605336795904770353, 60119367618216155944350400

Offset: 0

Author

Seiichi Manyama, Nov 30 2023

Keywords

• nonn

Links

• Eric Weisstein's World of Mathematics, Lambert W-Function.

Crossrefs

Cf. A052868, A362775, A367789.

Cf. A162475, A361283.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-x/(1-x)^4))))

Formula

E.g.f.: exp( -LambertW(-x/(1-x)^4) ).

a(n) = n! * Sum_{k=0..n} (k+1)^(k-1) * binomial(n+3*k-1,n-k)/k!.