A378046 E.g.f. satisfies A(x) = (1+x) * exp(x * A(x)^3 / (1+x)^2).

1, 2, 11, 169, 4049, 132881, 5542495, 280694135, 16730578625, 1147444968385, 89015365063991, 7707022678811567, 736734708409976017, 77070404075178587633, 8757816984586841345231, 1074244834335107678837191, 141469329806979182825146625, 19908315372027482035799282177

Offset

0,2

Links

Table of n, a(n) for n=0..17.

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

Formula

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

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

Prog

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

Crossrefs

Cf. A377826, A378045.

Cf. A363478.

Sequence in context: A067968 A295269 A197336 * A013050 A051255 A120445

Adjacent sequences: A378043 A378044 A378045 * A378047 A378048 A378049

Keyword

nonn

Author

Seiichi Manyama, Nov 15 2024

Status

approved