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

Author

Emanuele Munarini, Mar 12 2011

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A187646.

Programs

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}]

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

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