A375671 - OEIS

%I #12 Sep 01 2024 09:35:28

%S 1,0,4,6,88,420,5148,44520,587424,7203168,109106640,1689621120,

%T 29620245312,546547098240,10989238893696,233884517368320,

%U 5324618721070080,128058198711690240,3260308438558826496,87336328336058603520,2459915920512955929600

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

%F E.g.f.: B(x)^2, where B(x) is the e.g.f. of A052830.

%F a(n) = n! * Sum_{k=0..floor(n/2)} (k+1)! * |Stirling1(n-k,k)|/(n-k)!.

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

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

%Y Cf. A052830, A375672.

%Y Cf. A052801, A375660.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Aug 23 2024