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%I #17 Oct 22 2019 16:27:11
%S 1,6,36,250,2040,19334,209580,2562354,34915680,524986462,8636859924,
%T 154357103498,2978418173640,61718786864310,1367098836863868,
%U 32236969655283682,806313056758966320,21322699350055313678,594440128269066768612,17424632249851351374906
%N Third column (m=2) of triangle A129062 and second column of triangle A079641.
%H Seiichi Manyama, <a href="/A129063/b129063.txt">Table of n, a(n) for n = 0..422</a>
%F a(n) = A129062(n+2,2), n>=0.
%F a(n) = A079641(n+1,1), n>=0.
%F E.g.f.: (d^2/dx^2)((-log(2-exp(x)))^2)/2.
%F 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
%F 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
%o (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
%Y A000629 gives second, resp. first column of A129062, resp. A079641.
%Y Cf. A180875.
%K nonn,easy
%O 0,2
%A _Wolfdieter Lang_, May 04 2007