A362795 - OEIS

%I #14 May 04 2023 09:53:21

%S 1,1,0,0,24,0,-60,7980,-12992,-23184,10320480,-54616320,160009344,

%T 33740939232,-391545030240,3173349947040,211401523687680,

%U -4586955333880320,66611949275370240,2068372502060292864,-82278329345056212480,1885659676128917982720

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

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.

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

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

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

%Y Cf. A033917, A362794.

%Y Cf. A362798, A362800.

%K sign

%O 0,5

%A _Seiichi Manyama_, May 04 2023