A362381 E.g.f. satisfies A(x) = exp(x + x^3/6 * A(x)).

1, 1, 1, 2, 9, 41, 191, 1191, 9353, 77897, 704861, 7352621, 85323921, 1058023825, 14155416003, 206100005931, 3217934262481, 53320102598481, 939087824434009, 17562552535939705, 346668611080774081, 7196193133818592961, 156944931623033340711

Offset: 0

Author

Seiichi Manyama, Apr 20 2023

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..447
• Eric Weisstein's World of Mathematics, Lambert W-Function.

Crossrefs

Column k=1 of A362378.

Cf. A190865, A362477.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(-x^3/6*exp(x)))))

Formula

E.g.f.: exp(x - LambertW(-x^3/6 * exp(x))) = -6 * LambertW(-x^3/6 * exp(x))/x^3.

a(n) = n! * Sum_{k=0..floor(n/3)} (1/6)^k * (k+1)^(n-2*k-1) / (k! * (n-3*k)!).