%I #7 May 21 2014 16:42:40
%S 1,3,45,1340,62133,3926607,313159138,30077004204,3373855596485,
%T 432604296358341,62396125789568633,9997677582465775336,
%U 1761777732880595653932,338625441643226149909356,70500059235176885929427760
%N Convolution of the (signless) central Lah numbers (A187535) and the central Stirling numbers of the second kind (A007820).
%F a(n) = sum(Lah(2k,k)S(2n-2k,n-k)),k=0..n).
%F a(n) ~ 2^(4*n) * n^n / (exp(n) * sqrt(2*Pi*n)). - _Vaclav Kotesovec_, May 21 2014
%p L := n -> if n=0 then 1 else binomial(2*n-1,n-1)*(2*n)!/n! fi;
%p seq(sum(L(k)*combinat[stirling2](2*(n-k),n-k),k=0..n),n=0..12);
%t L[n_] := If[n == 0, 1, Binomial[2n - 1, n - 1](2n)!/n!]
%t Table[Sum[L[k]StirlingS2[2n - 2k, n - k], {k, 0, n}], {n, 0, 14}]
%o (Maxima) L(n):= if n=0 then 1 else binomial(2*n-1,n-1)*(2*n)!/n!;
%o makelist(sum(L(k)*stirling2(2*n-2*k,n-k),k,0,n),n,0,12);
%Y Cf. A187535, A007820.
%K nonn,easy
%O 0,2
%A _Emanuele Munarini_, Mar 12 2011