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 A187666 Binomial convolution of the (signless) central Lah numbers (A187535) and the (signless) central Stirling numbers of the first kind (A187646). 0

%I

%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

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Last modified August 12 00:34 EDT 2022. Contains 356067 sequences. (Running on oeis4.)