A351735 Expansion of e.g.f. 1/(1 - 3 * x)^x.

1, 0, 6, 27, 324, 4050, 64962, 1224720, 26776656, 665390376, 18529576200, 571602980520, 19349098690248, 713092338026640, 28422424039182768, 1218246132898693080, 55876497505161154560, 2730710993688989519040, 141654212475516155694528

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

a(n) = n! * Sum_{k=0..floor(n/2)} 3^(n-k) * |Stirling1(n-k,k)|/(n-k)!.

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-3*x)^x))
(PARI) a(n) = n!*sum(k=0, n\2, 3^(n-k)*abs(stirling(n-k, k, 1))/(n-k)!);

Crossrefs

Cf. A053490, A053491.

Sequence in context: A290802 A360754 A367886 * A322233 A164985 A367884

Adjacent sequences: A351732 A351733 A351734 * A351736 A351737 A351738

Keyword

nonn

Author

Seiichi Manyama, May 20 2022

Status

approved