cp's OEIS Frontend

A187666 Binomial convolution of the (signless) central Lah numbers (A187535) and the (signless) central Stirling numbers of the first kind (A187646).

%I A187666 #10 May 30 2025 05:24:09
%S A187666 1,3,51,1599,74545,4654255,365549495,34642467783,3846064986001,
%T A187666 489429448820811,70208261310969435,11205444535728231855,
%U A187666 1969021774778391995761,377672618542009829524551,78507169034687468202172591
%N A187666 Binomial convolution of the (signless) central Lah numbers (A187535) and the (signless) central Stirling numbers of the first kind (A187646).
%F A187666 a(n) = Sum_{k=0..n} binomial(n,k) * Lah(2k,k) * Stirling1(2n-2k,n-k).
%F A187666 a(n) ~ c * 2^(4*n + 1/2) * n^(n - 1/2) / (sqrt(Pi) * exp(n)), where c = Sum_{k>=0} abs(Stirling1(2*k,k)) / (k! * 2^(4*k+1)) = 0.550990257867992515027936630097897... - _Vaclav Kotesovec_, May 30 2025
%p A187666 L := n -> if n=0 then 1 else binomial(2*n-1,n-1)*(2*n)!/n! fi;
%p A187666 seq(sum(binomial(n,k)*L(k)*abs(combinat[stirling1](2*(n-k),n-k)),k=0..n),n=0..12);
%t A187666 L[n_] := If[n == 0, 1, Binomial[2n - 1, n - 1](2n)!/n!]
%t A187666 Table[Sum[Binomial[n,k]L[k]Abs[StirlingS1[2n - 2k, n - k]], {k, 0, n}], {n, 0, 14}]
%o A187666 (Maxima) L(n):= if n=0 then 1 else binomial(2*n-1,n-1)*(2*n)!/n!;
%o A187666 makelist(sum(binomial(n,k)*L(k)*abs(stirling1(2*n-2*k,n-k)),k,0,n),n,0,12);
%Y A187666 Cf. A187535, A187646.
%K A187666 nonn,easy
%O A187666 0,2
%A A187666 _Emanuele Munarini_, Mar 12 2011