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A370483
a(n) = Product_{k=0..n} binomial(n^2 + k^2, k^2).
0
1, 2, 350, 347633000, 101143578356902991250, 422044560230008480282938965899488406272, 1208807563912714402070105775158111317516306396248661153276031151000
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OFFSET
0,2
LINKS
Table of n, a(n) for n=0..6.
FORMULA
a(n) = Product_{k=0..n} binomial(n^2 + k^2, n^2).
a(n) =
A371643
(n) / ((n^2)!^(n+1) *
A255322
(n)).
a(n) ~ 2^(4*n^3/3 + n^2 + n/6 + 1/4) * exp((Pi-4)*n^3/3 + Pi*n/4) / (
A255504
* n^(n + 1/2) * Pi^(n/2)).
MATHEMATICA
Table[Product[Binomial[n^2 + k^2, n^2], {k, 0, n}], {n, 0, 8}]
Table[Product[Binomial[n^2 + k^2, k^2], {k, 0, n}], {n, 0, 8}]
CROSSREFS
Cf.
A255322
,
A371643
.
Sequence in context:
A063831
A216356
A064023
*
A179959
A024350
A012669
Adjacent sequences:
A370480
A370481
A370482
*
A370484
A370485
A370486
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec
, Mar 31 2024
STATUS
approved
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Last modified August 1 14:59 EDT 2024. Contains 374818 sequences. (Running on oeis4.)