A354123 - OEIS

%I #14 Nov 19 2023 08:22:06

%S 1,4,24,188,1804,20416,265640,3901320,63776280,1147796160,22540858080,

%T 479500074720,10980929163360,269298981833280,7040446188020160,

%U 195439047629422080,5740498087530831360,177855276360034736640,5796391124741936993280

%N Expansion of e.g.f. 1/(1 + log(1 - x))^4.

%F a(n) = (1/6) * Sum_{k=0..n} (k + 3)! * |Stirling1(n,k)|.

%F a(n) ~ sqrt(Pi/2) * n^(n + 7/2) / (3 * (exp(1) - 1)^(n+4)). - _Vaclav Kotesovec_, Jun 04 2022

%F a(0) = 1; a(n) = Sum_{k=1..n} (3*k/n + 1) * (k-1)! * binomial(n,k) * a(n-k). - _Seiichi Manyama_, Nov 19 2023

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+log(1-x))^4))

%o (PARI) a(n) = sum(k=0, n, (k+3)!*abs(stirling(n, k, 1)))/6;

%Y Cf. A007840, A052801, A354122.

%Y Cf. A226738, A354121.

%K nonn

%O 0,2

%A _Seiichi Manyama_, May 17 2022