A354286 Expansion of e.g.f. 1/(1 - x)^(2/(1 + 2 * log(1-x))).

1, 2, 14, 144, 1936, 32000, 625952, 14117152, 360175584, 10246079616, 321313928448, 11006050602624, 408662128569984, 16344011453662464, 700254206319007488, 31990601456727585792, 1551985176120589820928, 79669906174753878177792

Offset

0,2

Links

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

Formula

a(0) = 1; a(n) = Sum_{k=1..n} A088500(k) * binomial(n-1,k-1) * a(n-k).

a(n) = Sum_{k=0..n} 2^k * A000262(k) * |Stirling1(n,k)|.

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

Prog

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

Crossrefs

Cf. A088815, A354287.

Cf. A000262, A088500, A354288, A354290.

Sequence in context: A100510 A354290 A346433 * A346432 A333592 A087132

Adjacent sequences: A354283 A354284 A354285 * A354287 A354288 A354289

Keyword

nonn

Author

Seiichi Manyama, May 23 2022

Status

approved