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A187545 Stirling transform (of the first kind) of the central Lah numbers (A187535).

%I A187545 #20 Apr 10 2018 10:13:38
%S A187545 1,2,38,1312,66408,4442088,369791064,36848702784,4277191653888,
%T A187545 566809715422464,84441103242634176,13970100487593468480,
%U A187545 2541362625439551554880,504185908064687887996800,108336183242510523080868480
%N A187545 Stirling transform (of the first kind) of the central Lah numbers (A187535).
%H A187545 Vincenzo Librandi, <a href="/A187545/b187545.txt">Table of n, a(n) for n = 0..200</a>
%F A187545 a(n) = sum(s(n,k)*L(k), k=0..n), where s(n,k) are the (signless) Stirling numbers of the first kind and L(n) are the central Lah numbers.
%F A187545 E.g.f.: 1/2 + 1/Pi*K(-16*log(1-x)), where K(z) is the elliptic integral of the first kind (defined as in Mathematica).
%F A187545 a(n) ~ n! / (2*Pi*n * (1 - exp(-1/16))^n). - _Vaclav Kotesovec_, Apr 10 2018
%p A187545 lahc := n -> if n=0 then 1 else binomial(2*n-1,n-1)*(2*n)!/n! fi;
%p A187545 seq(add(abs(combinat[stirling1](n,k))*lahc(k), k=0..n), n=0..20);
%t A187545 lahc[n_] := If[n == 0, 1, Binomial[2n - 1, n - 1](2n)!/n!]
%t A187545 Table[Sum[Abs[StirlingS1[n, k]]*lahc[k], {k, 0, n}], {n, 0, 20}]
%o A187545 (Maxima) lahc(n):= if n=0 then 1 else binomial(2*n-1,n-1)*(2*n)!/n!;
%o A187545 makelist(sum(abs(stirling1(n,k))*lahc(k),k,0,n),n,0,12);
%Y A187545 Cf. A187536, A008297, A111596, A187536, A187538, A187539, A187540, A187542, A187543, A187544, A187546, A187547, A187548.
%K A187545 nonn,easy,nice
%O A187545 0,2
%A A187545 _Emanuele Munarini_, Mar 11 2011