A376437 - OEIS

%I #12 Sep 23 2024 09:28:15

%S 1,0,0,18,36,120,24300,192024,1572480,194205600,3380922720,

%T 50671716480,4879442177280,144175221440640,3391736273557632,

%U 287077095515548800,12328722259931750400,413067654425986560000,33216197499043235527680

%N Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 + x^2*log(1-x))^3 ).

%H <a href="/index/Res#revert">Index entries for reversions of series</a>

%F E.g.f. A(x) satisfies A(x) = 1/(1 + x^2*A(x)^2 * log(1 - x*A(x)))^3.

%F a(n) = (3 * n!/(3*n+3)!) * Sum_{k=0..floor(n/3)} (3*n+k+2)! * |Stirling1(n-2*k,k)|/(n-2*k)!.

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1+x^2*log(1-x))^3)/x))

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

%Y Cf. A376386, A376393.

%Y Cf. A375679.

%K nonn

%O 0,4

%A _Seiichi Manyama_, Sep 22 2024