A365038 E.g.f. satisfies A(x) = exp(x * (1 + x)/A(x)).

1, 1, 1, -2, 9, -44, 175, 246, -21007, 396712, -5576769, 57840850, -151112951, -14137899060, 539212013327, -13335393617714, 239914650459105, -1990873438067504, -76974185162417921, 5220283004540970282, -194958036625254566599, 5226632355735840377140

Offset: 0

Author

Seiichi Manyama, Aug 18 2023

Keywords

• sign
• easy

Links

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

Crossrefs

Cf. A362771, A362773, A363478, A365039, A365040.

Cf. A361067.

Programs

PARI

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

Formula

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

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