A263430 a(n) = Product_{k=0..n} (4*k+1)^(n-k).

1, 1, 5, 225, 131625, 1309010625, 273380323978125, 1427352844030287890625, 216119240915841469025244140625, 1079864992142473709995957417730712890625, 199639840782299404795675492100337942688751220703125

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..36

Eric Weisstein's World of Mathematics, Catalan's Constant

Eric Weisstein's World of Mathematics, Glaisher-Kinkelin Constant

Formula

a(n) ~ A^(1/8) * 2^(n^2 + 3*n/2 + 1/8) * Pi^(n/2 + 1/8) * n^(n^2/2 + n/4 - 5/96) / (Gamma(1/4)^(n + 1/4) * exp(3*n^2/4 + n/4 + 1/96 - C/(4*Pi))), where A = A074962 is the Glaisher-Kinkelin constant and C = A006752 = is Catalan's constant.

Mathematica

Table[Product[(4*k+1)^(n-k), {k, 0, n}], {n, 0, 10}]

Prog

(PARI) for(n=0, 10, print1(prod(k=0, n, (4*k+1)^(n-k)), ", ")) \\ G. C. Greubel, Aug 25 2018
(Magma) [(&*[(4*k+1)^(n-k): k in [0..n]]): n in [0..10]]; // G. C. Greubel, Aug 25 2018

Crossrefs

Cf. A000178, A057863, A263416.

Sequence in context: A225818 A185551 A324098 * A339311 A200988 A201491

Adjacent sequences: A263427 A263428 A263429 * A263431 A263432 A263433

Keyword

nonn

Author

Vaclav Kotesovec, Oct 18 2015

Status

approved