A187656 Convolution of the (signless) central Stirling numbers of the first kind (A187646).

1, 2, 23, 472, 14109, 557138, 27417263, 1617536576, 111304630793, 8752522524930, 774271257457719, 76102169738598232, 8227653697751043061, 970337814111625277394, 123968202132756025685151, 17055359730313188973301568

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) / (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))*abs(combinat[stirling1](2*(n-k), n-k)), k=0..n), n=0..12);

Mathematica

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

Prog

(Maxima) makelist(sum(abs(stirling1(2*k, k))*abs(stirling1(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, 1))); \\ Michel Marcus, May 28 2017

Crossrefs

Cf. A187646.

Sequence in context: A074649 A233211 A134355 * A350376 A255907 A360239

Adjacent sequences: A187653 A187654 A187655 * A187657 A187658 A187659

Keyword

nonn,easy

Author

Emanuele Munarini, Mar 12 2011

Status

approved