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A324403 a(n) = Product_{i=1..n, j=1..n} (i^2 + j^2). 34
1, 2, 400, 121680000, 281324160000000000, 15539794609114833408000000000000, 49933566483104048708063697937367040000000000000000, 19323883089768863178599626514889213871887405416448000000000000000000000000 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Next term is too long to be included.
LINKS
FORMULA
a(n) ~ 2^(n*(n+1) - 3/4) * exp(Pi*n*(n+1)/2 - 3*n^2 + Pi/12) * n^(2*n^2 - 1/2) / (Pi^(1/4) * Gamma(3/4)).
a(n) = 2*n^2*a(n-1)*Product_{i=1..n-1} (n^2 + i^2)^2. - Chai Wah Wu, Feb 26 2019
For n>0, a(n)/a(n-1) = A272244(n)^2 / (2*n^6). - Vaclav Kotesovec, Dec 02 2023
MAPLE
a:= n-> mul(mul(i^2+j^2, i=1..n), j=1..n):
seq(a(n), n=0..7); # Alois P. Heinz, Jun 24 2023
MATHEMATICA
Table[Product[i^2+j^2, {i, 1, n}, {j, 1, n}], {n, 1, 10}]
PROG
(PARI) a(n) = prod(i=1, n, prod(j=1, n, i^2+j^2)); \\ Michel Marcus, Feb 27 2019
(Python)
from math import prod, factorial
def A324403(n): return (prod(i**2+j**2 for i in range(1, n) for j in range(i+1, n+1))*factorial(n))**2<<n # Chai Wah Wu, Nov 22 2023
CROSSREFS
Sequence in context: A249177 A249178 A281650 * A214597 A283661 A067827
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Feb 26 2019
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Jun 24 2023
STATUS
approved

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Last modified February 27 09:47 EST 2024. Contains 370374 sequences. (Running on oeis4.)