A375660 - OEIS

%I #12 Sep 13 2025 11:23:37

%S 1,0,4,6,80,370,4152,34034,413632,4744674,66354680,954512482,

%T 15454225536,263909265074,4898255210968,96284064551250,

%U 2022022344889472,44858682139345090,1052826609589372152,25994393541984673154,674563101823606851520,18337775305498096349202

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

%F E.g.f.: B(x)^2, where B(x) is the e.g.f. of A052848.

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

%t With[{nn=30},CoefficientList[Series[1/(1-x*(Exp[x]-1))^2,{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Sep 13 2025 *)

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

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

%Y Cf. A052848, A375661.

%Y Cf. A005649.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Aug 23 2024