OFFSET
0,4
FORMULA
a(n) = n! * Sum_{k=0..floor(n/3)} (n-k+1)^(k-1) * Stirling2(n-2*k,k)/(n-2*k)!.
MATHEMATICA
m = 21; (* number of terms *)
A[_] = 0;
Do[A[x_] = Exp[x^2*(Exp[x*A[x]] - 1)*A[x]] + O[x]^m // Normal, {m}];
CoefficientList[A[x], x]*Range[0, m - 1]! (* Jean-François Alcover, Sep 12 2022 *)
PROG
(PARI) a(n) = n!*sum(k=0, n\3, (n-k+1)^(k-1)*stirling(n-2*k, k, 2)/(n-2*k)!);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 07 2022
STATUS
approved