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A294323
a(n) = Product_{k=0..n} (5*k + 1)!.
4
1, 720, 28740096000, 601322989968949248000000, 30722158107023001697205508762501120000000000, 12389984031943899068723274670059592852478855603111854080000000000000000
OFFSET
0,2
FORMULA
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.
A268506(n) * A294323(n) * A294324(n) * A294325(n) * A294326(n) = A000178(5*n+4).
MATHEMATICA
Table[Product[(5*k + 1)!, {k, 0, n}] , {n, 0, 10}]
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Oct 28 2017
STATUS
approved