A365056 E.g.f. satisfies A(x) = exp( x * (1+x/2)/A(x) ).

1, 1, 0, 1, -6, 46, -440, 5076, -68740, 1070056, -18835164, 369994780, -8025080096, 190501729848, -4912802070280, 136775150153656, -4088669684755440, 130620500241909376, -4441243727496127184, 160132524268963159440, -6102784264210449418144

Offset

0,5

Links

Seiichi Manyama, Table of n, a(n) for n = 0..403

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

Formula

E.g.f.: exp( LambertW(x * (1+x/2)) ).

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

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(lambertw(x*(1+x/2)))))

Crossrefs

Cf. A365053, A365054, A365055.

Cf. A365038.

Sequence in context: A052781 A284109 A049378 * A218497 A261499 A001829

Adjacent sequences: A365053 A365054 A365055 * A365057 A365058 A365059

Keyword

sign

Author

Seiichi Manyama, Aug 19 2023

Status

approved