A087152 - OEIS

%I #12 May 24 2017 21:18:59

%S 1,3,20,194,2554,42226,843744,19769256,531768120,16152296424,

%T 546895099200,20425461026736,834215500905552,36988602430554576,

%U 1769524998544143360,90851799797294235264,4982968503277896871296

%N Expansion of (1-sqrt(1-4*log(1+x)))/log(1+x)/2.

%H G. C. Greubel, <a href="/A087152/b087152.txt">Table of n, a(n) for n = 1..370</a>

%F a(n) = Sum_{k=0..n} Stirling1(n, k)*k!*Catalan(k).

%F a(n) ~ 2*n! / (exp(1/8)*sqrt(Pi) * (exp(1/4)-1)^(n-1/2) * n^(3/2)). - _Vaclav Kotesovec_, May 03 2015

%t Rest[CoefficientList[Series[(1-Sqrt[1-4*Log[1+x]])/Log[1+x]/2, {x, 0, 20}], x] * Range[0, 20]!] (* _Vaclav Kotesovec_, May 03 2015 *)

%o (PARI) x='x+O('x^50); Vec(serlaplace((1-sqrt(1-4*log(1+x)))/log(1+x)/2 - 1)) \\ _G. C. Greubel_, May 24 2017

%Y Cf. A000108, A052851, A052803, A052886, A052895, A006531, A048287.

%K nonn

%O 1,2

%A _Vladeta Jovovic_, Oct 18 2003