|
|
A325050
|
|
a(n) = Product_{k=0..n} (k!^2 + 1).
|
|
1
|
|
|
2, 4, 20, 740, 426980, 6148938980, 3187616116170980, 80970552724144881738980, 131634021973939424914920841290980, 17333817381151204925617274632152908873802980, 228254990993381085562170532497621436371926846785405002980
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
LINKS
|
|
|
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|