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A187659
Convolution of the (signless) central Stirling numbers of the first kind (A187646) and the central Stirling numbers of the second kind (A007820).
1
1, 2, 19, 333, 8862, 322885, 15061381, 858280605, 57766424400, 4479377168841, 392785285842806, 38393983653735732, 4136603248470746422, 486806030644218961182, 62109988002922704031388, 8537900524822110186179616
OFFSET
0,2
LINKS
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
MAPLE
seq(sum(abs(combinat[stirling1](2*k, k))*combinat[stirling2](2*(n-k), n-k), k=0..n), n=0..12);
MATHEMATICA
Table[Sum[Abs[StirlingS1[2k, k]]StirlingS2[2n - 2k, n - k], {k, 0, n}], {n, 0, 15}]
PROG
(Maxima) makelist(sum(abs(stirling1(2*k, k))*stirling2(2*n-2*k, n-k), k, 0, n), n, 0, 12);
(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
CROSSREFS
Sequence in context: A119773 A137647 A233107 * A308330 A078369 A090308
KEYWORD
nonn,easy
AUTHOR
Emanuele Munarini, Mar 12 2011
STATUS
approved