A354291 Expansion of e.g.f. exp(f(x) - 1) where f(x) = 1/(4 - 3*exp(x)) = e.g.f. for A032033.

1, 3, 30, 435, 8211, 190056, 5196099, 163541055, 5815620696, 230350071189, 10048990989747, 478467217544322, 24678559536271581, 1370217125170670367, 81457311857722336614, 5160975525978898855143, 347090708803947931122807, 24690132231344937537382560

Offset

0,2

Links

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

Formula

a(0) = 1; a(n) = Sum_{k=1..n} A032033(k) * binomial(n-1,k-1) * a(n-k).

a(n) = Sum_{k=0..n} 3^k * A000262(k) * Stirling2(n,k).

a(n) ~ exp(-7/8 - n + 1/(8*log(4/3)) + sqrt(n/log(4/3))) * n^(n - 1/4) / (2*log(4/3)^(n + 1/4)). - Vaclav Kotesovec, May 23 2022

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(3*(exp(x)-1)/(4-3*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, 3^k*k!*stirling(j, k, 2))*binomial(i-1, j-1)*v[i-j+1])); v;

Crossrefs

Cf. A075729, A354290.

Cf. A032033, A354287, A354289.

Sequence in context: A336538 A294240 A007004 * A354287 A276361 A360973

Adjacent sequences: A354288 A354289 A354290 * A354292 A354293 A354294

Keyword

nonn

Author

Seiichi Manyama, May 23 2022

Status

approved