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A367542
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a(n) = Product_{i=1..n, j=1..n} (i^2 + i*j + j^2).
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13
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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) ~ c * 3^(3*n*(n+1)/2) * n^(2*n^2 - 2/3) / exp(3*n^2 - Pi*n*(n+1) / (2*sqrt(3))), where c = 3^(5/12) * exp(Pi/(12*sqrt(3))) * Gamma(1/3) / (2^(4/3) * Pi^(4/3)) = 0.42478290981890921418850643030484274341562970375995548434917...
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MATHEMATICA
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Table[Product[Product[(i^2 + i*j + j^2), {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 A367542(n): return (prod(i*(i+j)+j**2 for i in range(1, n) for j in range(i+1, n+1))*factorial(n))**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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