A294323 -id:A294323 - cp's OEIS frontend

A294324 a(n) = Product_{k=0..n} (5*k + 2)!.

2, 10080, 4828336128000, 1717378459351319052288000000, 1930334638180469242638816526565470371840000000000, 21019161870767674789722561439867977128887689291877548419973120000000000000000

Offset: 0

Vaclav Kotesovec, Oct 28 2017

nonn

Cf. A268506, A294319, A294321, A294323, A294325, A294326.

Table[Product[(5*k + 2)!, {k, 0, n}] , {n, 0, 10}]
FoldList[Times,(5Range[0,10]+2)!] (* Harvey P. Dale, Aug 11 2024 *)

a(n) ~ 2^(n/2 + 6/5) * 5^(5*n^2/2 + 5*n + 7/3) * n^(5*n^2/2 + 5*n + 137/60) * Pi^(n/2 + 11/10) / (A^(1/5) * (1 + sqrt(5))^(1/10) * Gamma(1/5)^(2/5) * Gamma(2/5)^(4/5) * exp(15*n^2/4 + 5*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).

A294325 a(n) = Product_{k=0..n} (5*k + 3)!.

Original entry on oeis.org

6, 241920, 1506440871936000, 9644797427717007797649408000000, 249337464544494851133170653103408676989829120000000000, 76020086814652932482688746849816272353956621412690696880710462996480000000000000000

Offset: 0

Vaclav Kotesovec, Oct 28 2017

nonn

Cf. A268506, A294322, A294323, A294324, A294326.

Table[Product[(5*k + 3)!, {k, 0, n}] , {n, 0, 10}]

a(n) ~ (1 + sqrt(5))^(2/5) * Gamma(2/5)^(1/5) * 2^(n/2 + 1/5) * 5^(5*n^2/2 + 6*n + 43/12) * n^(5*n^2/2 + 6*n + 203/60) * Pi^(n/2 + 3/5) / (A^(1/5) * Gamma(1/5)^(2/5) * exp(15*n^2/4 + 6*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).

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

Original entry on oeis.org

24, 8709120, 759246199455744000, 92358580167818066670290731008000000, 57303733451473984666829812178837795780510487674880000000000

Offset: 0

Vaclav Kotesovec, Oct 28 2017

nonn

Cf. A268506, A294323, A294324, A294325.

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

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).

cp's OEIS Frontend

A294324 a(n) = Product_{k=0..n} (5*k + 2)!.

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A294325 a(n) = Product_{k=0..n} (5*k + 3)!.

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

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