A362794 E.g.f. satisfies A(x) = (1+x)^(A(x)^x).

1, 1, 0, 6, 0, 170, -120, 12446, -35336, 1832400, -12172320, 469680552, -5524990416, 189586178184, -3321122831208, 111608536026360, -2599887499382400, 90253048158627072, -2595580675897337856, 95720854442948910720, -3237436187047116892800

Offset: 0

Author

Seiichi Manyama, May 04 2023

Keywords

• sign

Links

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

Crossrefs

Cf. A033917, A362795.

Cf. A362796, A362799.

Cf. A349504, A349505.

Programs

PARI

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

Formula

E.g.f.: exp( -LambertW(-x * log(1+x)) / x ) = (1+x)^exp( -LambertW(-x * log(1+x)) ).

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