%I #8 Apr 17 2022 22:46:55
%S 1,3,51,1599,74545,4654255,365549495,34642467783,3846064986001,
%T 489429448820811,70208261310969435,11205444535728231855,
%U 1969021774778391995761,377672618542009829524551,78507169034687468202172591
%N Binomial convolution of the (signless) central Lah numbers (A187535) and the (signless) central Stirling numbers of the first kind (A187646).
%F a(n) = Sum_{k=0..n} binomial(n,k) * Lah(2k,k) * Stirling1(2n-2k,n-k).
%p L := n -> if n=0 then 1 else binomial(2*n-1,n-1)*(2*n)!/n! fi;
%p seq(sum(binomial(n,k)*L(k)*abs(combinat[stirling1](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[Binomial[n,k]L[k]Abs[StirlingS1[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(binomial(n,k)*L(k)*abs(stirling1(2*n-2*k,n-k)),k,0,n),n,0,12);
%Y Cf. A187535, A187646.
%K nonn,easy
%O 0,2
%A _Emanuele Munarini_, Mar 12 2011