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%I #16 Apr 26 2021 20:02:31
%S 1,2,10,76,772,9808,149552,2660544,54093696,1237306560,31446049728,
%T 879119219328,26811313164672,885830291432448,31518653868782592,
%U 1201567079771092992,48860409899753588736,2111033523652100407296
%N Expansion of e.g.f. 1/(1+2*log(1-x)).
%H Andrew Howroyd, <a href="/A088500/b088500.txt">Table of n, a(n) for n = 0..200</a>
%F a(n) = Sum_{k=0..n} |Stirling1(n, k)|*k!*2^k.
%F a(n) ~ n! * exp(n/2) / (2 * (exp(1/2)-1)^(n+1)). - _Vaclav Kotesovec_, May 03 2015
%F a(0) = 1; a(n) = 2 * Sum_{k=0..n-1} binomial(n,k) * (n-k-1)! * a(k). - _Ilya Gutkovskiy_, Apr 26 2021
%t CoefficientList[Series[1/(1+2*Log[1-x]), {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, May 03 2015 *)
%o (PARI) my(x='x+O('x^30)); Vec(serlaplace(1/(1+2*log(1-x)))) \\ _Michel Marcus_, Apr 26 2021
%Y Cf. A007840, A088501.
%K easy,nonn
%O 0,2
%A _Vladeta Jovovic_, Nov 12 2003
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