A306760
a(n) = Product_{i=1..n, j=1..n} (i*j + 1).
Original entry on oeis.org
1, 2, 90, 705600, 4105057320000, 52487876090562232320000, 3487017405172854771910634342400000000, 2448893405298238642974553493547144534294528000000000000, 33257039167768610289435138215602132823918399655132218973388800000000000000000
Offset: 0
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a:= n-> mul(mul(i*j+1, i=1..n), j=1..n):
seq(a(n), n=0..9); # Alois P. Heinz, Jun 24 2023
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Table[Product[i*j + 1, {i, 1, n}, {j, 1, n}], {n, 1, 10}]
Table[n!^(2*n) * Product[Binomial[n + 1/j, n], {j, 1, n}], {n, 1, 10}]
A324590
a(n) = n!^(4*n) * Product_{k=1..n} binomial(n + 1/k^2, n).
Original entry on oeis.org
1, 2, 1080, 16133644800, 139256878046022696960000, 6288402750181849898716908922601472000000000, 8322157105451357856813375261666887975745751468393837363200000000000000
Offset: 0
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a:= n-> n!^(4*n)*mul(binomial(n+1/k^2, n), k=1..n):
seq(a(n), n=0..7); # Alois P. Heinz, Jun 24 2023
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Table[n!^(4*n) * Product[Binomial[1/k^2 + n, n], {k, 1, n}], {n, 1, 8}]
A324596
a(n) = n!^(3*n) * Product_{k=1..n} binomial(n + 1/k^2, n).
Original entry on oeis.org
1, 2, 270, 74692800, 419731620267960000, 252716802910471719823692648960000, 59736659298524125157504488525739821430187940800000000, 16079377413231597423103950774423398920424350187193326745026311068057600000000000
Offset: 0
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a:= n-> n!^(3*n)*mul(binomial(n+1/k^2, n), k=1..n):
seq(a(n), n=0..7); # Alois P. Heinz, Jun 24 2023
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Table[n!^(3*n) * Product[Binomial[n + 1/k^2, n], {k, 1, n}], {n, 1, 8}]
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