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A324403
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a(n) = Product_{i=1..n, j=1..n} (i^2 + j^2).
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34
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1, 2, 400, 121680000, 281324160000000000, 15539794609114833408000000000000, 49933566483104048708063697937367040000000000000000, 19323883089768863178599626514889213871887405416448000000000000000000000000
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OFFSET
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0,2
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COMMENTS
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Next term is too long to be included.
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LINKS
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FORMULA
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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
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MAPLE
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a:= n-> mul(mul(i^2+j^2, i=1..n), j=1..n):
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MATHEMATICA
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Table[Product[i^2+j^2, {i, 1, n}, {j, 1, n}], {n, 1, 10}]
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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