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A367550
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a(n) = Product_{i=1..n, j=1..n} (i^4 + i^2*j^2 + j^4).
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5
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OFFSET
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1,1
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LINKS
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FORMULA
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a(n) ~ Gamma(1/3)^3 * 3^(3*n*(n+1)/2 + 7/12) * n^(4*n^2 - 1) / (8*Pi^3 * exp(6*n^2 - (6*n*(n+1) + 1)*Pi/(4*sqrt(3)))).
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MATHEMATICA
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Table[Product[Product[i^4 + i^2*j^2 + j^4, {i, 1, n}], {j, 1, n}], {n, 1, 10}]
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PROG
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(Python)
from math import prod, factorial
def A367550(n): return (prod((i2:=i**2)*(i2+(j2:=j**2))+j2**2 for i in range(1, n) for j in range(i+1, n+1))*factorial(n)**2)**2*3**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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STATUS
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approved
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