A354289 - OEIS

%I #14 May 23 2022 09:46:22

%S 1,3,24,276,4086,73620,1557702,37770138,1030916484,31245154164,

%T 1040274476208,37716394860936,1478413316987424,62274364390387656,

%U 2804282634867538248,134397620584518275928,6828489621874434752208,366547074721109281366128

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

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

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

%F 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

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace((1+x)^(3/(1-3*log(1+x)))))

%o (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;

%Y Cf. A088819, A354288.

%Y Cf. A000262, A335531, A354287, A354291.

%K nonn

%O 0,2

%A _Seiichi Manyama_, May 23 2022