A362795 E.g.f. satisfies A(x) = (1+x)^(A(x)^(x^2)).

1, 1, 0, 0, 24, 0, -60, 7980, -12992, -23184, 10320480, -54616320, 160009344, 33740939232, -391545030240, 3173349947040, 211401523687680, -4586955333880320, 66611949275370240, 2068372502060292864, -82278329345056212480, 1885659676128917982720

Offset: 0

Author

Seiichi Manyama, May 04 2023

Keywords

• sign

Links

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

Crossrefs

Cf. A033917, A362794.

Cf. A362798, A362800.

Programs

PARI

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

Formula

E.g.f.: exp( -LambertW(-x^2 * log(1+x)) / x^2 ) = (1+x)^exp( -LambertW(-x^2 * log(1+x)) ).

E.g.f.: Sum_{k>=0} (k*x^2 + 1)^(k-1) * (log(1+x))^k / k!.