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A356785
E.g.f. satisfies log(A(x)) = x * (exp(x*A(x)) - 1) * A(x).
13
1, 0, 2, 3, 64, 365, 7356, 85687, 1920752, 34821369, 905128300, 22172123171, 672107454888, 20552960420005, 721088019634724, 26257726364294895, 1053711696230404576, 44336326818388565105, 2010106841636689325532, 95747319823049127621019
OFFSET
0,3
FORMULA
a(n) = n! * Sum_{k=0..floor(n/2)} (n+1)^(k-1) * Stirling2(n-k,k)/(n-k)!.
E.g.f.: (1/x) * Series_Reversion( x*exp(x*(1 - exp(x))) ). - Seiichi Manyama, Sep 21 2024
MATHEMATICA
nmax = 19; A[_] = 1;
Do[A[x_] = Exp[x*(Exp[x*A[x]]-1)*A[x]] + O[x]^(nmax+1) // Normal, {nmax}];
CoefficientList[A[x], x]*Range[0, nmax]! (* Jean-François Alcover, Mar 04 2024 *)
PROG
(PARI) a(n) = n!*sum(k=0, n\2, (n+1)^(k-1)*stirling(n-k, k, 2)/(n-k)!);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 27 2022
STATUS
approved