A118790 Secondary diagonal of triangle A118788.

1, 3, 23, 255, 3679, 65247, 1371887, 33347535, 919848991, 28382683263, 968565339983, 36217270235055, 1472548026160639, 64679673007670367, 3052084360057720367, 153980839859926277775, 8270901171633696369631

Offset: 0

Author

Paul D. Hanna, Apr 29 2006

Keywords

• nonn
• changed

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A118788, A118789.

Programs

Mathematica

Table[(n+1)! * SeriesCoefficient[(x/(2*x + Log[1-x]))^(n+2),{x,0,n}], {n,0,20}] (* Vaclav Kotesovec, Sep 01 2025 *)

PARI

{a(n)=local(x=X+X^2*O(X^(n)));(n+1)!*polcoeff((x/(2*x+log(1-x)))^(n+2),n,X)}

Formula

a(n) = (n+1)!*[x^n] ( x/(2*x + log(1-x)) )^(n+2).

a(n) ~ n^(n+1) / (4 * exp(n) * (1 - log(2))^(n + 3/2)). - Vaclav Kotesovec, Sep 01 2025