A354289 Expansion of e.g.f. (1 + x)^(3/(1 - 3 * log(1+x))).

1, 3, 24, 276, 4086, 73620, 1557702, 37770138, 1030916484, 31245154164, 1040274476208, 37716394860936, 1478413316987424, 62274364390387656, 2804282634867538248, 134397620584518275928, 6828489621874434752208, 366547074721109281366128

Offset

0,2

Links

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

Formula

a(0) = 1; a(n) = Sum_{k=1..n} A335531(k) * binomial(n-1,k-1) * a(n-k).

a(n) = Sum_{k=0..n} 3^k * A000262(k) * Stirling1(n,k).

a(n) ~ exp(-11/12 + 1/(6*(exp(1/3) - 1)) + 2*exp(1/6)*sqrt(n)/sqrt(3*(exp(1/3) - 1)) - n) * n^(n - 1/4) / (sqrt(2) * 3^(1/4) * (exp(1/3) - 1)^(n + 1/4)). - Vaclav Kotesovec, May 23 2022

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace((1+x)^(3/(1-3*log(1+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, 1))*binomial(i-1, j-1)*v[i-j+1])); v;

Crossrefs

Cf. A088819, A354288.

Cf. A000262, A335531, A354287, A354291.

Sequence in context: A352278 A218223 A276360 * A351763 A355794 A355426

Adjacent sequences: A354286 A354287 A354288 * A354290 A354291 A354292

Keyword

nonn

Author

Seiichi Manyama, May 23 2022

Status

approved