A088501 Expansion of e.g.f. 1/(1-2*log(1+x)).

1, 2, 6, 28, 172, 1328, 12272, 132480, 1633344, 22663104, 349324608, 5923548288, 109570736256, 2195765044224, 47386235513856, 1095689316882432, 27023900076988416, 708173307424456704, 19649589144733089792

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..419

Formula

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

a(n) ~ n! * exp(1/2) / (2 * (exp(1/2)-1)^(n+1)). - Vaclav Kotesovec, May 03 2015

a(0) = 1; a(n) = 2 * Sum_{k=1..n} (-1)^(k-1) * (k-1)! * binomial(n,k) * a(n-k). - Seiichi Manyama, May 22 2022

Mathematica

CoefficientList[Series[1/(1-2*Log[1+x]), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, May 03 2015 *)

Prog

(PARI) a(n) = sum(k=0, n, k!*2^k*stirling(n, k, 1)); \\ Seiichi Manyama, Feb 03 2022
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-2*log(1+x)))) \\ Seiichi Manyama, Feb 03 2022
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=2*sum(j=1, i, (-1)^(j-1)*(j-1)!*binomial(i, j)*v[i-j+1])); v; \\ Seiichi Manyama, May 22 2022

Crossrefs

Column k=2 of A320080.

Sequence in context: A345367 A156626 A207386 * A140092 A052809 A136631

Adjacent sequences: A088498 A088499 A088500 * A088502 A088503 A088504

Keyword

easy,nonn

Author

Vladeta Jovovic, Nov 12 2003

Status

approved