A354290 Expansion of e.g.f. exp(f(x) - 1) where f(x) = 1/(3 - 2*exp(x)).

1, 2, 14, 142, 1878, 30494, 585398, 12946910, 323717622, 9020101470, 276940926646, 9283709731806, 337237965060982, 13191050077634654, 552593521885522486, 24677110613547498718, 1169994350288769049334, 58684818937875321715038

Offset

0,2

Links

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

Formula

a(0) = 1; a(n) = Sum_{k=1..n} A004123(k+1) * binomial(n-1,k-1) * a(n-k).

a(n) = Sum_{k=0..n} 2^k * A000262(k) * Stirling2(n,k).

a(n) ~ exp(1/(6*log(3/2)) - 5/6 + 2*sqrt(n)/sqrt(3*log(3/2)) - n) * (n^(n - 1/4) / (sqrt(2) * 3^(1/4) * log(3/2)^(n + 1/4))). - Vaclav Kotesovec, May 23 2022

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(2*(exp(x)-1)/(3-2*exp(x)))))
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, sum(k=0, j, 2^k*k!*stirling(j, k, 2))*binomial(i-1, j-1)*v[i-j+1])); v;

Crossrefs

Cf. A075729, A354291.

Cf. A004123, A354286, A354288.

Sequence in context: A361638 A271564 A100510 * A346433 A354286 A346432

Adjacent sequences: A354287 A354288 A354289 * A354291 A354292 A354293

Keyword

nonn

Author

Seiichi Manyama, May 23 2022

Status

approved