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A322252
a(0) = 1 and a(n) = (5*n)!/(5!*n!^5) for n > 0.
5
1, 1, 945, 1401400, 2546168625, 5194672859376, 11423951396577720, 26478825654361766400, 63805953776276649848625, 158421985022100255941485000, 402789797982510165934296910320, 1044048983553856888083223814102400, 2749848597736878877579660426025283000
OFFSET
0,3
FORMULA
O.g.f.: F({1/5, 2/5, 3/5, 4/5}, {1, 1, 1}, 3125*x)/(120*x), where F is the generalized hypergeometric function. - Stefano Spezia, Dec 01 2018
a(n) = (1/5!)*A008978(n) for n >= 1. - Peter Bala, Feb 18 2020
MATHEMATICA
a[n_]:=(5*n)!/(5!*n!^5); Array[a, 20] (* or *) CoefficientList[Series[HypergeometricPFQ[{1/5, 2/5, 3/5, 4/5}, {1, 1, 1}, 3125 x]/(120 x) , {x, 0, 20}], x] (* Stefano Spezia, Dec 01 2018 *)
PROG
(Magma) [1] cat [Factorial(5*n)/(120*Factorial(n)^5):n in [1..12]]; // Marius A. Burtea, Feb 18 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 30 2018
STATUS
approved