A204515 a(n) = (2*n)! * (2*n+1)! / ((n+1)^2 * n!^3).

1, 3, 40, 1050, 42336, 2328480, 163088640, 13913499600, 1401656256000, 162984589447680, 21497802046156800, 3172717285311974400, 518147911684085760000, 92790773980160256000000, 18083066033253630689280000, 3810158522787893903827200000

Offset: 0

Author

Reinhard Zumkeller, Oct 19 2014

Keywords

• nonn

Comments

Central terms of the triangle A247500.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..250
• G.-N. Han and H. Xiong, Difference operators for partitions and some applications, arXiv preprint arXiv:1508.00772 [math.CO], 2015-2018.

Crossrefs

Cf. A000142, A247500, A248045.

Programs

Haskell

a204515 n = a247500 (2 * n) n

Mathematica

Table[((2n)!(2n+1)!)/((n+1)^2 n!^3),{n,0,20}] (* Harvey P. Dale, May 17 2019 *)

PARI

a(n) = (2*n)! * (2*n+1)! / ((n+1)^2 * n!^3); \\ Michel Marcus, Feb 03 2022

Formula

a(n) = A248045(n+1) / (n+1).