A129063 Third column (m=2) of triangle A129062 and second column of triangle A079641.

1, 6, 36, 250, 2040, 19334, 209580, 2562354, 34915680, 524986462, 8636859924, 154357103498, 2978418173640, 61718786864310, 1367098836863868, 32236969655283682, 806313056758966320, 21322699350055313678, 594440128269066768612, 17424632249851351374906

Offset: 0

Author

Wolfdieter Lang, May 04 2007

Keywords

• nonn
• easy

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..422

Crossrefs

A000629 gives second, resp. first column of A129062, resp. A079641.

Cf. A180875.

Programs

PARI

N=20; x='x+O('x^N); f=exp(x)/(2-exp(x)); Vec(serlaplace(deriv(f*intformal(f)))) \\ Seiichi Manyama, Oct 22 2019

Formula

a(n) = A129062(n+2,2), n>=0.

a(n) = A079641(n+1,1), n>=0.

E.g.f.: (d^2/dx^2)((-log(2-exp(x)))^2)/2.

E.g.f.: d/dx (f(x) * Integral f(x) dx), where f(x) = exp(x)/(2-exp(x)), cf. A000629. - Seiichi Manyama, Oct 22 2019

a(n) ~ n! * n * log(n) / (log(2))^(n+2) * (1 + (gamma - log(2) - log(log(2))) / log(n)), where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Oct 22 2019