A371196 - OEIS

%I #12 Jun 04 2024 12:13:57

%S 1,0,2,9,56,570,5844,75600,1101568,18059328,330859440,6657765840,

%T 146394716544,3488742148320,89569620370944,2464853317748640,

%U 72368541315763200,2258038571305305600,74611690018599389184,2602671162733649456640,95577054989820127994880

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

%F a(n) = n! * Sum_{j=0..n} Sum_{k=0..j} k! * binomial(j,n-j-k) * |Stirling1(j,k)|/j!.

%t With[{nn=20},CoefficientList[Series[1/(1+x*Log[1-x-x^2]),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Jun 04 2024 *)

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

%Y Cf. A331339, A371197, A371198.

%Y Cf. A088369.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Mar 15 2024