A354314 Expansion of e.g.f. 1/(1 - x/3 * (exp(3 * x) - 1)).

1, 0, 2, 9, 60, 495, 4986, 58401, 780984, 11749779, 196446870, 3612882933, 72484364052, 1575418827879, 36875093680530, 924769734574185, 24737895033896304, 703105981990977915, 21159355356941587470, 672148402091190649629, 22475238194908656800460

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Formula

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

a(n) = n! * Sum_{k=0..floor(n/2)} 3^(n-2*k) * k! * Stirling2(n-k,k)/(n-k)!.

Prog

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

Crossrefs

Cf. A052848, A354313.

Cf. A288834, A328182, A353999, A354312.

Sequence in context: A363390 A205570 A116364 * A354496 A357683 A120970

Adjacent sequences: A354311 A354312 A354313 * A354315 A354316 A354317

Keyword

nonn

Author

Seiichi Manyama, May 23 2022

Status

approved