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A367679
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a(n) = Product_{i=1..n, j=1..n} (i^4 - i^3*j + i^2*j^2 - i*j^3 + j^4).
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2
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1, 1936, 1765124816400, 19271059559619728900751360000, 25048411180596698786915756280274804766474649600000000, 23045227505577134384745253646275782332295626096040088365089618773238077194240000000000
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) ~ c * n^(4*n^2 - 5/6) * phi^(sqrt(5)*n*(n+1)) / exp(6*n^2 - sqrt(phi)*Pi*n*(n+1)/5^(1/4)), where phi = A001622 is the golden ratio and c = 0.2505211390193028244009922677012518708897316924498037078191143761182342931773594...
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MATHEMATICA
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Table[Product[i^4 - i^3*j + i^2*j^2 - i*j^3 + j^4, {i, 1, n}, {j, 1, n}], {n, 1, 6}]
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PROG
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(Python)
from math import prod, factorial
def A367679(n): return (prod(i*(i*(i*(i-j)+j**2)-j**3)+j**4 for i in range(1, n) for j in range(i+1, n+1))*factorial(n)**2)**2 # Chai Wah Wu, Nov 26 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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