A351428 - OEIS

%I #15 Feb 11 2022 17:14:43

%S 1,-1,-3,-11,-41,-75,1540,37725,657715,10551750,163089430,2407275470,

%T 31865298262,290682880132,-2479867505029,-267542605513289,

%U -11438897571729494,-404343336811199242,-13192591498632627584,-410340915410006575406,-12233989907129223814578

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

%F a(n) = T(n,5), T(n,k) = Sum_{j=0..n} Stirling2(n,j) * T(j,k-1), k>1, T(n,0) = (-1)^n * n!.

%p g:= x-> exp(x)-1:

%p a:= n-> n! * coeff(series(1/((g@@5)(x)+1), x, n+1), x, n):

%p seq(a(n), n=0..20);  # _Alois P. Heinz_, Feb 11 2022

%t T[n_, 0] := (-1)^n * n!; T[n_, k_] := T[n, k] = Sum[StirlingS2[n, j]*T[j, k - 1], {j, 0, n}]; a[n_] := T[n, 5]; Array[a, 20, 0] (* _Amiram Eldar_, Feb 11 2022 *)

%o (PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(1/exp(exp(exp(exp(exp(x)-1)-1)-1)-1)))

%o (PARI) T(n, k) = if(k==0, (-1)^n*n!, sum(j=0, n, stirling(n, j, 2)*T(j, k-1)));

%o a(n) = T(n, 5);

%Y Column k=5 of A351429.

%Y Cf. A000587, A130410, A351427.

%Y Cf. A000357, A351423.

%K sign

%O 0,3

%A _Seiichi Manyama_, Feb 11 2022