A354287 Expansion of e.g.f. 1/(1 - x)^(3/(1 + 3 * log(1-x))).

1, 3, 30, 438, 8334, 194580, 5368662, 170591022, 6126386724, 245127214548, 10804866210648, 519910458588576, 27105081897342816, 1521393008601586536, 91445577404393807928, 5858664681621903625368, 398467273528657973600208, 28668189882264862351707504

Offset

0,2

Links

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

Formula

a(0) = 1; a(n) = Sum_{k=1..n} A354263(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((-5 + 1/(exp(1/3) - 1) + 4*sqrt(3*n/(exp(1/3) - 1)) - 4*n)/6) * 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/(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!*abs(stirling(j, k, 1)))*binomial(i-1, j-1)*v[i-j+1])); v;

Crossrefs

Cf. A088815, A354286.

Cf. A000262, A354263, A354289, A354291.

Sequence in context: A294240 A007004 A354291 * A276361 A360973 A359972

Adjacent sequences: A354284 A354285 A354286 * A354288 A354289 A354290

Keyword

nonn

Author

Seiichi Manyama, May 23 2022

Status

approved