A362244 - OEIS

%I #11 Dec 27 2024 16:13:32

%S 1,1,2,12,60,440,3810,37212,430696,5482080,78252390,1227201140,

%T 20955546348,388492703040,7745445183658,165550236166980,

%U 3773990094033360,91401848785134272,2344168680183033678,63455096201600595060,1808160553359068792020

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

%F a(n) = n! * Sum_{i=0..n} (-1)^(n-i) * ( Sum_{j=0..n-i} i^j * Stirling2(n-i-j,j)/(n-i-j)! ).

%t With[{nn=20},CoefficientList[Series[1/(1-x Exp[-x(Exp[-x]-1)]),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Dec 27 2024 *)

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

%Y Cf. A362245, A362246, A362247.

%Y Cf. A362237.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Apr 12 2023