A294326 a(n) = Product_{k=0..n} (5*k + 4)!.

24, 8709120, 759246199455744000, 92358580167818066670290731008000000, 57303733451473984666829812178837795780510487674880000000000

Offset: 0

Author

Vaclav Kotesovec, Oct 28 2017

Keywords

• nonn

Crossrefs

Cf. A268506, A294323, A294324, A294325.

Programs

Mathematica

Table[Product[(5*k + 4)!, {k, 0, n}] , {n, 0, 10}]
FoldList[Times,(5*Range[0,5]+4)!] (* Harvey P. Dale, Sep 27 2018 *)

Formula

a(n) ~ 2^(n/2 + 1/5) * 5^(5*n^2/2 + 7*n + 29/6) * n^(5*n^2/2 + 7*n + 281/60) * Pi^(n/2 + 1/10) * Gamma(1/5)^(3/5) * Gamma(2/5)^(1/5) / (A^(1/5) * (1 + sqrt(5))^(1/10) * exp(15*n^2/4 + 7*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).