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

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..250

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

Cf. A007820, A187646.

Sequence in context: A119773 A137647 A233107 * A308330 A078369 A090308

Adjacent sequences: A187656 A187657 A187658 * A187660 A187661 A187662

Keyword

nonn,easy

Author

Emanuele Munarini, Mar 12 2011

Status

approved