A365037 E.g.f. satisfies A(x) = exp(x * (1 + x/A(x)^3)).

1, 1, 3, -11, -11, 1341, -14339, -168923, 8905065, -85313735, -4604578919, 197455645641, -273728455571, -267002430142187, 9427821270512373, 178475402982086701, -28273343910563670959, 713736314833387866225, 51907546734507018043057

Offset

0,3

Links

Table of n, a(n) for n=0..18.

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

Formula

E.g.f.: exp( x + LambertW(3*x^2*exp(-3*x))/3 ).

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

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x+lambertw(3*x^2*exp(-3*x))/3)))

Crossrefs

Cf. A125500, A143768, A363354, A363529, A365035, A365036.

Cf. A361092.

Sequence in context: A232038 A072980 A128500 * A043051 A024545 A101134

Adjacent sequences: A365034 A365035 A365036 * A365038 A365039 A365040

Keyword

sign

Author

Seiichi Manyama, Aug 17 2023

Status

approved