A354310 Expansion of e.g.f. 1/(1 - 3*x)^(x/3).

1, 0, 2, 9, 84, 990, 14754, 264600, 5549424, 133217784, 3601384200, 108249692760, 3580724721672, 129250420556400, 5055196156459344, 212951257371183240, 9612027759287831040, 462798880374787387200, 23675607840207619145664, 1282413928716141429168000

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Formula

a(0) = 1; a(n) = (n-1)! * Sum_{k=2..n} k * 3^(k-2)/(k-1) * a(n-k)/(n-k)!.

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

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-3*x)^(x/3)))
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=(i-1)!*sum(j=2, i, j*3^(j-2)/(j-1)*v[i-j+1]/(i-j)!)); v;
(PARI) a(n) = n!*sum(k=0, n\2, 3^(n-2*k)*abs(stirling(n-k, k, 1))/(n-k)!);

Crossrefs

Cf. A066166, A354309.

Cf. A351735, A354316, A354320.

Sequence in context: A069234 A086929 A193466 * A262011 A120959 A125797

Adjacent sequences: A354307 A354308 A354309 * A354311 A354312 A354313

Keyword

nonn

Author

Seiichi Manyama, May 23 2022

Status

approved