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

0,3

Links

Table of n, a(n) for n=0..21.

Formula

a(n) = n! * Sum_{k=0..floor(n/2)} 2^k * Stirling2(n-k,k)/(n-k)!.

Prog

(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)!);

Crossrefs

Cf. A052506, A351734.

Cf. A053489, A351736.

Sequence in context: A012910 A259133 A131847 * A089630 A058162 A244388

Adjacent sequences: A351730 A351731 A351732 * A351734 A351735 A351736

Keyword

nonn

Author

Seiichi Manyama, May 20 2022

Status

approved