A351733 Expansion of e.g.f. exp( 2 * x * (exp(x) - 1) ).
1, 0, 4, 6, 56, 250, 1812, 12614, 101040, 864882, 7988780, 78726142, 823897032, 9111774698, 106068603396, 1295153135670, 16538681229152, 220281968528098, 3053087839536732, 43941561067048430, 655501502129291640, 10118103843683127642
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(2*x*(exp(x)-1)))) -
PARI
a(n) = n!*sum(k=0, n\2, 2^k*stirling(n-k, k, 2)/(n-k)!);
Formula
a(n) = n! * Sum_{k=0..floor(n/2)} 2^k * Stirling2(n-k,k)/(n-k)!.