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

0,2

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.

Formula

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

Mathematica

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

Prog

(Haskell)
a204515 n = a247500 (2 * n) n
(PARI) a(n) = (2*n)! * (2*n+1)! / ((n+1)^2 * n!^3); \\ Michel Marcus, Feb 03 2022

Crossrefs

Cf. A000142, A247500, A248045.

Sequence in context: A358368 A260754 A047799 * A012250 A094330 A110468

Adjacent sequences: A204512 A204513 A204514 * A204516 A204517 A204518

Keyword

nonn

Author

Reinhard Zumkeller, Oct 19 2014

Status

approved