A375699 - OEIS

%I #12 Aug 25 2024 09:58:15

%S 1,0,0,0,4,10,40,210,5264,45360,409800,4065600,77948640,1183422240,

%T 17527233360,267109642800,5422495921920,110998923235200,

%U 2270809072896000,47142009514454400,1116394268619772800,27963045712157472000,718066383283082803200

%N Expansion of e.g.f. 1 / (1 + x^3 * log(1 - x))^(1/6).

%F a(n) = n! * Sum_{k=0..floor(n/4)} (Product_{j=0..k-1} (6*j+1)) * |Stirling1(n-3*k,k)|/(6^k*(n-3k)!).

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x^3*log(1-x))^(1/6)))

%o (PARI) a(n) = n!*sum(k=0, n\4, prod(j=0, k-1, 6*j+1)*abs(stirling(n-3*k, k, 1))/(6^k*(n-3*k)!));

%Y Cf. A351504, A375700, A375701.

%Y Cf. A008542, A351506.

%K nonn

%O 0,5

%A _Seiichi Manyama_, Aug 25 2024