OFFSET
0,5
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..247
FORMULA
a(n) = T(n,n), T(n,k) = Sum_{j=0..n} Stirling2(n,j) * T(j,k-1), k>1, T(n,0) = (-1)^n * n!.
MAPLE
g:= x-> exp(x)-1:
a:= n-> n! * coeff(series(1/(1+(g@@n)(x)), x, n+1), x, n):
seq(a(n), n=0..22); # Alois P. Heinz, Feb 11 2022
MATHEMATICA
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, n]; Array[a, 17, 0] (* Amiram Eldar, Feb 11 2022 *)
PROG
(PARI) T(n, k) = if(k==0, (-1)^n*n!, sum(j=0, n, stirling(n, j, 2)*T(j, k-1)));
a(n) = T(n, n);
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Feb 11 2022
STATUS
approved