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%I #20 May 22 2022 09:50:04
%S 1,2,6,28,172,1328,12272,132480,1633344,22663104,349324608,5923548288,
%T 109570736256,2195765044224,47386235513856,1095689316882432,
%U 27023900076988416,708173307424456704,19649589144733089792
%N Expansion of e.g.f. 1/(1-2*log(1+x)).
%H Seiichi Manyama, <a href="/A088501/b088501.txt">Table of n, a(n) for n = 0..419</a>
%F a(n) = Sum_{k=0..n} Stirling1(n, k)*k!*2^k.
%F a(n) ~ n! * exp(1/2) / (2 * (exp(1/2)-1)^(n+1)). - _Vaclav Kotesovec_, May 03 2015
%F 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
%t CoefficientList[Series[1/(1-2*Log[1+x]), {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, May 03 2015 *)
%o (PARI) a(n) = sum(k=0, n, k!*2^k*stirling(n, k, 1)); \\ _Seiichi Manyama_, Feb 03 2022
%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-2*log(1+x)))) \\ _Seiichi Manyama_, Feb 03 2022
%o (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
%Y Column k=2 of A320080.
%K easy,nonn
%O 0,2
%A _Vladeta Jovovic_, Nov 12 2003
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