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%I #32 Sep 08 2022 08:46:23
%S 1,1,945,1401400,2546168625,5194672859376,11423951396577720,
%T 26478825654361766400,63805953776276649848625,
%U 158421985022100255941485000,402789797982510165934296910320,1044048983553856888083223814102400,2749848597736878877579660426025283000
%N a(0) = 1 and a(n) = (5*n)!/(5!*n!^5) for n > 0.
%F 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
%F a(n) = (1/5!)*A008978(n) for n >= 1. - _Peter Bala_, Feb 18 2020
%t 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 *)
%o (Magma) [1] cat [Factorial(5*n)/(120*Factorial(n)^5):n in [1..12]]; // _Marius A. Burtea_, Feb 18 2020
%Y Row 5 of A060540.
%Y Cf. A000142, A100734, A008978, A060542, A082368.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Nov 30 2018