|
| |
|
|
A324596
|
|
a(n) = n!^(3*n) * Product_{k=1..n} binomial(n + 1/k^2, n).
|
|
2
|
|
|
|
2, 270, 74692800, 419731620267960000, 252716802910471719823692648960000, 59736659298524125157504488525739821430187940800000000, 16079377413231597423103950774423398920424350187193326745026311068057600000000000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
LINKS
|
Table of n, a(n) for n=1..7.
|
|
|
FORMULA
|
a(n) ~ n!^(3*n) * n^(Pi^2/6) / A303670.
a(n) ~ n^(3*n*(2*n+1)/2 + Pi^2/6) * (2*Pi)^(3*n/2) / exp(3*n^2 - 1/4 - gamma*Pi^2/6 + c), where gamma is the Euler-Mascheroni constant A001620 and c = A306774 = Sum_{k>=2} (-1)^k * Zeta(k) * Zeta(2*k) / k.
|
|
|
MATHEMATICA
|
Table[n!^(3*n) * Product[Binomial[n + 1/k^2, n], {k, 1, n}], {n, 1, 8}]
|
|
|
CROSSREFS
|
Cf. A303670, A306760, A306774, A324589, A324597.
Sequence in context: A188964 A278771 A318171 * A007512 A048534 A135696
Adjacent sequences: A324593 A324594 A324595 * A324597 A324598 A324599
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Vaclav Kotesovec, Mar 09 2019
|
|
|
STATUS
|
approved
|
| |
|
|
