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A306642
a(n) = Sum_{k=0..n} (3*n)!/(k! * (n-k)!)^3.
3
1, 12, 900, 94080, 11988900, 1704214512, 260453217024, 41886697881600, 6996546610936740, 1203384096358158000, 211855235800656848400, 38011289046678107596800, 6928290032159649797280000, 1279703438754969901486464000, 239070018975087493229806080000
OFFSET
0,2
LINKS
Robert W. Donley Jr, Directed path enumeration for semi-magic squares of size three, arXiv:2107.09463 [math.CO], 2021.
FORMULA
a(n) ~ 216^n / (Pi*n)^2. - Vaclav Kotesovec, Jun 21 2021
MATHEMATICA
Array[Sum[(3 #)!/(k!*(# - k)!)^3, {k, 0, #}] &, 15, 0] (* Michael De Vlieger, Dec 02 2021 *)
PROG
(PARI) {a(n) = sum(k=0, n, (3*n)!/(k!*(n-k)!)^3)}
CROSSREFS
Column 3 of A306641.
Sequence in context: A276013 A116225 A214313 * A283570 A159870 A283040
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 02 2019
STATUS
approved