A375903 - OEIS

%I #11 Sep 02 2024 08:38:29

%S 1,-3,9,-18,-57,942,-4299,-33078,786267,-4357818,-84919647,2153185746,

%T -9754462833,-539983739298,13389257569005,-13826647549926,

%U -6661768436593725,153336015047780790,938088731006163417,-139051687661849130654,2787586449012275332023

%N E.g.f. satisfies A(x) = (2 - exp(x * A(x)^(1/3)))^3.

%F E.g.f.: A(x) = ( (1/x) * Series_Reversion(x / (2 - exp(x))) )^3.

%F a(n) = 3 * (n+2)! * Sum_{k=0..n} (-1)^k * Stirling2(n,k)/(n-k+3)!.

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace((serreverse(x/(2-exp(x)))/x)^3))

%o (PARI) a(n) = 3*(n+2)!*sum(k=0, n, (-1)^k*stirling(n, k, 2)/(n-k+3)!);

%Y Cf. A097718, A362354, A375898.

%K sign

%O 0,2

%A _Seiichi Manyama_, Sep 02 2024