A306642 a(n) = Sum_{k=0..n} (3*n)!/(k! * (n-k)!)^3.

1, 12, 900, 94080, 11988900, 1704214512, 260453217024, 41886697881600, 6996546610936740, 1203384096358158000, 211855235800656848400, 38011289046678107596800, 6928290032159649797280000, 1279703438754969901486464000, 239070018975087493229806080000

Offset: 0

Author

Seiichi Manyama, Mar 02 2019

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..431
• Robert W. Donley Jr, Directed path enumeration for semi-magic squares of size three, arXiv:2107.09463 [math.CO], 2021.

Crossrefs

Column 3 of A306641.

Programs

Mathematica

Array[Sum[(3 #)!/(k!*(# - k)!)^3, {k, 0, #}] &, 15, 0] (* Michael De Vlieger, Dec 02 2021 *)

PARI

{a(n) = sum(k=0, n, (3*n)!/(k!*(n-k)!)^3)}

Formula

a(n) ~ 216^n / (Pi*n)^2. - Vaclav Kotesovec, Jun 21 2021