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A306728
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a(n) = Product_{i=1..n, j=1..n} (i*(i+1) + j*(j+1)).
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1
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1, 4, 3072, 4682022912, 62745927042654535680, 22033340103629170301586112512000000, 479715049773154880180722813201712394999926095872000000, 1318058833735625830065875826842622254472987373414662267314001234660163584000000
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) ~ c * 2^(n*(n+2)) * exp(Pi*n*(n+2)/2 - 3*n^2) * n^(2*n^2 - 2 - Pi/4), where c = 0.4952828896469310726828820344381813905230827930914109676983577406850360879...
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MATHEMATICA
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Table[Product[i*(i+1)+j*(j+1), {i, 1, n}, {j, 1, n}], {n, 0, 8}]
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PROG
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(Python)
from math import prod, factorial
def A306728(n): return (prod(i*(i+1)+j*(j+1) for i in range(1, n) for j in range(i+1, n+1))*factorial(n))**2*(n+1)<<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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