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A294320 a(n) = Product_{k=0..n} (4*k + 1)!. 4
1, 120, 43545600, 271159356948480000, 96447974277170077976494080000000, 4927617876373416030299815278723491640115200000000000, 76433315893700635598991132508610825923227961061372903345356800000000000000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..6.

FORMULA

a(n) ~ 2^(4*n^2 + 15*n/2 + 10/3) * n^(2*n^2 + 7*n/2 + 65/48) * Pi^(n/2 + 3/4) / (A^(1/4) * Gamma(1/4)^(1/2) * exp(3*n^2 + 7*n/2 - 1/48)), where A is the Glaisher-Kinkelin constant A074962.

A268505(n) * A294320(n) * A294321(n) * A294322(n) = A000178(4*n + 3).

MATHEMATICA

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

CROSSREFS

Cf. A168467, A268505, A294318, A294321, A294322.

Sequence in context: A210279 A172626 A258926 * A268506 A172730 A045509

Adjacent sequences:  A294317 A294318 A294319 * A294321 A294322 A294323

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Oct 28 2017

STATUS

approved

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Last modified November 16 04:54 EST 2018. Contains 317257 sequences. (Running on oeis4.)