A368323 Expansion of e.g.f. exp(3*x) / (4 - 3*exp(x)).

1, 6, 48, 516, 7212, 125436, 2616348, 63662556, 1770359772, 55384885596, 1925211581148, 73613650011996, 3070625126631132, 138757783222353756, 6752624341715261148, 352087859568330751836, 19582053567267458627292, 1157162515572965014445916

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Formula

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

a(n) = (64/27)*A032033(n) - (1/3)*(2^n + 4/3 + (16/9)*0^n).

Prog

(PARI) b(n, t) = sum(k=0, n, t^k*k!*stirling(n, k, 2));
a(n, m=3, t=3) = my(u=1+1/t); u^m*b(n, t)-(1/t)*sum(j=0, m-1, u^j*(m-1-j)^n);

Crossrefs

Cf. A032033, A201354, A368322, A368324.

Sequence in context: A053506 A052567 A351340 * A002170 A153467 A354750

Adjacent sequences: A368320 A368321 A368322 * A368324 A368325 A368326

Keyword

nonn

Author

Seiichi Manyama, Dec 21 2023

Status

approved