A246606 Central terms of the triangle A116853.

1, 4, 78, 3216, 229080, 25022880, 3884393520, 812752093440, 220448163358080, 75225258805132800, 31537353006189676800, 15933924342019634227200, 9548252826112300306406400, 6695627848564821490753228800, 5431772705577464891946292992000, 5047432593984519350928894369792000

Offset: 1

Author

Reinhard Zumkeller, Aug 31 2014

Keywords

• nonn

Comments

a(n) = A116853(2*n,n).

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A000142, A116853.

Programs

Haskell

a246606 n = a116853 (2 * n - 1) n

Maple

a := n -> (2*n - 1)!*hypergeom([1 - n], [1 - 2*n], -1):
seq(simplify(a(n)), n=1..15); # Peter Luschny, Nov 04 2018

Formula

a(n) = (2*n - 1)!*hypergeom([1 - n], [1 - 2*n], -1). - Peter Luschny, Nov 04 2018

Conjecture: D-finite with recurrence +(-2*n+3)*a(n) +4*(n-1)*(2*n^2-4*n+1)*a(n-1) +(n-1)*(n-2)*(2*n-1)*a(n-2)=0. - R. J. Mathar, Jul 01 2022

a(n) ~ sqrt(Pi) * 2^(2*n) * n^(2*n - 1/2) / exp(2*n + 1/2). - Vaclav Kotesovec, Mar 08 2023