A377895 E.g.f. satisfies A(x) = (1 + x) * exp(x * A(x)^3).

1, 2, 15, 283, 8057, 313161, 15436735, 922964771, 64910124753, 5250807814753, 480339263735831, 49032749858906067, 5525542086267361801, 681359718334607629409, 91259859216031641999375, 13193464971338727171704611, 2047721360761921797402720545, 339610337568547449759788735553

Offset: 0

Author

Seiichi Manyama, Nov 11 2024

Keywords

• nonn

Links

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

Crossrefs

Cf. A377826, A377894.

Programs

PARI

a(n) = n!*sum(k=0, n, (3*k+1)^(k-1)*binomial(3*k+1, n-k)/k!);

Formula

E.g.f.: (1+x) * exp( -LambertW(-3*x*(1+x)^3)/3 ).

E.g.f.: ( -LambertW(-3*x*(1+x)^3)/(3*x) )^(1/3).

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