A294323 - OEIS

%I #5 Oct 28 2017 10:55:40

%S 1,720,28740096000,601322989968949248000000,

%T 30722158107023001697205508762501120000000000,

%U 12389984031943899068723274670059592852478855603111854080000000000000000

%N a(n) = Product_{k=0..n} (5*k + 1)!.

%F a(n) ~ 2^(n/2 + 7/10) * 5^(5*n^2/2 + 4*n + 4/3) * n^(5*n^2/2 + 4*n + 83/60) * Pi^(n/2 + 3/5) * Gamma(2/5)^(1/5) / (A^(1/5) * (1 + sqrt(5))^(1/10) * Gamma(1/5)^(2/5) * exp(15*n^2/4 + 4*n - 1/60)), where A is the Glaisher-Kinkelin constant A074962.

%F A268506(n) * A294323(n) * A294324(n) * A294325(n) * A294326(n) = A000178(5*n+4).

%t Table[Product[(5*k + 1)!, {k, 0, n}] , {n, 0, 10}]

%Y Cf. A168467, A268506, A294318, A294320, A294324, A294325, A294326.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Oct 28 2017