A383208 Expansion of e.g.f. (exp(f(x)) - 1)^3 / 6, where f(x) = (exp(2*x) - 1)/2.

0, 0, 0, 1, 18, 245, 3120, 39697, 517790, 6999785, 98520060, 1445923149, 22129416210, 352932509085, 5859167661256, 101122879922313, 1811960841148774, 33662625853200337, 647550189266734452, 12881675626292023173, 264677402162135670554, 5610552395871699336453

Offset

0,5

Links

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

Formula

a(n) = Sum_{k=3..n} 2^(n-k) * Stirling2(n,k) * Stirling2(k,3).

Prog

(PARI) a(n) = sum(k=3, n, 2^(n-k)*stirling(n, k, 2)*stirling(k, 3, 2));

Crossrefs

Column k=3 of A383206.

Cf. A000559.

Sequence in context: A016186 A016294 A153593 * A001713 A110395 A153600

Adjacent sequences: A383205 A383206 A383207 * A383209 A383210 A383211

Keyword

nonn

Author

Seiichi Manyama, Apr 19 2025

Status

approved