A362799 E.g.f. satisfies A(x) = exp( (exp(x) - 1) * A(x)^x ).

1, 1, 2, 11, 63, 542, 5183, 62211, 830252, 12900381, 220566835, 4223662522, 88001471869, 2007052809465, 49309469989666, 1306455781607975, 36973887007453315, 1116728635342926570, 35775769695237122035, 1213704083311914974899

Offset: 0

Author

Seiichi Manyama, May 04 2023

Keywords

• nonn

Links

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

Crossrefs

Cf. A052880, A362800.

Cf. A362794, A362796.

Cf. A000110, A361777.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-x*(exp(x)-1))/x)))

Formula

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

E.g.f.: Sum_{k>=0} (k*x + 1)^(k-1) * (exp(x) - 1)^k / k!.