A362392 E.g.f. satisfies A(x) = exp(x + x^3 * A(x)).

1, 1, 1, 7, 49, 241, 2041, 26041, 282913, 3449377, 57170161, 973059121, 16847893921, 343341027745, 7680743819113, 175958943331081, 4375517632543681, 118932887426911681, 3374685950589927649, 100735118425384221025, 3217474234925998764481

Offset: 0

Author

Seiichi Manyama, Apr 20 2023

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..414
• Eric Weisstein's World of Mathematics, Lambert W-Function.

Crossrefs

Column k=6 of A362378.

Cf. A118395, A125500, A362393, A362430.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(-x^3*exp(x)))))

Formula

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

a(n) = n! * Sum_{k=0..floor(n/3)} (k+1)^(n-2*k-1) / (k! * (n-3*k)!).