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Binomial convolution of the (signless) central Stirling numbers of the first kind (A187646).
0

%I #10 Oct 19 2024 03:59:38

%S 1,2,24,516,16064,655840,33157240,1999679696,140128848384,

%T 11189643689088,1003005057594240,99725721676986240,

%U 10892178742891589792,1296379044138734510656,166999512859041432577280,23149972436862049305233280

%N Binomial convolution of the (signless) central Stirling numbers of the first kind (A187646).

%F a(n) = Sum_{k=0..n} binomial(n,k)*s(2*k,k)*s(2*n-2*k,n-k).

%p seq(sum(binomial(n,k)*abs(combinat[stirling1](2*k,k))*abs(combinat[stirling1](2*(n-k),n-k)),k=0..n),n=0..12);

%t Table[Sum[Binomial[n, k]Abs[StirlingS1[2k, k]]Abs[StirlingS1[2n - 2k, n - k]], {k, 0, n}], {n, 0, 15}]

%o (Maxima) makelist(sum(binomial(n,k)*abs(stirling1(2*k,k))*abs(stirling1(2*n-2*k,n-k)),k,0,n),n,0,12);

%Y Cf. A187646.

%K nonn,easy

%O 0,2

%A _Emanuele Munarini_, Mar 12 2011