A325050 - OEIS

A325050

a(n) = Product_{k=0..n} (k!^2 + 1).

2, 4, 20, 740, 426980, 6148938980, 3187616116170980, 80970552724144881738980, 131634021973939424914920841290980, 17333817381151204925617274632152908873802980, 228254990993381085562170532497621436371926846785405002980

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,1

LINKS

Table of n, a(n) for n=0..10.

FORMULA

a(n) ~ c * n^(n^2 + 2*n + 5/6) * (2*Pi)^(n+1) / (A^2 * exp(3*n^2/2 + 2*n - 1/6)), where c = Product_{k>=0} (1 + 1/k!^2) = 5.1481781945902396880952694880498895... and A is the Glaisher-Kinkelin constant A074962.

MATHEMATICA

Table[Product[k!^2 + 1, {k, 0, n}], {n, 0, 12}]

Table[BarnesG[n+2]^2 * Product[1 + 1/k!^2, {k, 0, n}], {n, 0, 12}]

CROSSREFS

Cf. A055209, A101686, A217757, A238695, A325048.

Sequence in context: A228808 A059588 A132498 * A325503 A087314 A326972

Adjacent sequences: A325047 A325048 A325049 * A325051 A325052 A325053

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Mar 26 2019

STATUS

approved