A355508 E.g.f. satisfies log(A(x)) = x^2 * (exp(x * A(x)) - 1) * A(x).
1, 0, 0, 6, 12, 20, 1830, 15162, 82376, 3326472, 59467050, 678585710, 20553790092, 563969783676, 10776243950654, 318310813941330, 10988438698692240, 303144002003606672, 9910024990673571666, 392381835437286982998, 14072003919511407720020
Offset: 0
Keywords
Programs
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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 *) -
PARI
a(n) = n!*sum(k=0, n\3, (n-k+1)^(k-1)*stirling(n-2*k, k, 2)/(n-2*k)!);
Formula
a(n) = n! * Sum_{k=0..floor(n/3)} (n-k+1)^(k-1) * Stirling2(n-2*k,k)/(n-2*k)!.