A187659 Convolution of the (signless) central Stirling numbers of the first kind (A187646) and the central Stirling numbers of the second kind (A007820).
1, 2, 19, 333, 8862, 322885, 15061381, 858280605, 57766424400, 4479377168841, 392785285842806, 38393983653735732, 4136603248470746422, 486806030644218961182, 62109988002922704031388, 8537900524822110186179616
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..250
Programs
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Maple
seq(sum(abs(combinat[stirling1](2*k,k))*combinat[stirling2](2*(n-k),n-k),k=0..n),n=0..12);
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Mathematica
Table[Sum[Abs[StirlingS1[2k, k]]StirlingS2[2n - 2k, n - k], {k, 0, n}], {n, 0, 15}] -
Maxima
makelist(sum(abs(stirling1(2*k,k))*stirling2(2*n-2*k,n-k),k,0,n),n,0,12);
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PARI
a(n) = sum(k=0, n, abs(stirling(2*k, k, 1)*stirling(2*(n-k), n-k, 2))); \\ Michel Marcus, May 28 2017
Formula
a(n) = Sum_{k=0..n} s(2*k,k)*S(2*n-2*k,n-k).
a(n) ~ n^n * c^(2*n) * 2^(3*n-1) / (sqrt(Pi*(c-1)*n) * exp(n) * (2*c-1)^n), where c = -LambertW(-1,-exp(-1/2)/2). - Vaclav Kotesovec, May 21 2014