A324439
a(n) = Product_{i=1..n, j=1..n} (i^6 + j^6).
Original entry on oeis.org
1, 2, 1081600, 528465082730906880000, 29276520893554373473343522853366005760000000000, 5719545329208791496596894540018824083491259163047733746620041978183680000000000000000
Offset: 0
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a:= n-> mul(mul(i^6 + j^6, i=1..n), j=1..n):
seq(a(n), n=0..5); # Alois P. Heinz, Nov 26 2023
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Table[Product[i^6 + j^6, {i, 1, n}, {j, 1, n}], {n, 1, 6}]
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from math import prod, factorial
def A324439(n): return (prod(i**6+j**6 for i in range(1,n) for j in range(i+1,n+1))*factorial(n)**3)**2<Chai Wah Wu, Nov 26 2023
A367550
a(n) = Product_{i=1..n, j=1..n} (i^4 + i^2*j^2 + j^4).
Original entry on oeis.org
3, 63504, 2260442279270448, 3379470372507391964272022793486336, 2097229364987262298214192667129919538956418868293588090880000
Offset: 1
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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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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
A203675
Vandermonde sequence using x^2 - xy + y^2 applied to (1,4,9,...,n^2).
Original entry on oeis.org
1, 13, 57889, 560058939856, 42130404012097952586256, 65111467563626175389271488157658681344, 4528499444374253250530486688998183592108605307719698157568
Offset: 1
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f[j_] := j^2; z = 12;
u[n_] := Product[f[j]^2 - f[j] f[k] + f[k]^2, {j, 1, k - 1}]
v[n_] := Product[u[n], {k, 2, n}]
Table[v[n], {n, 1, z}] (* A203675 *)
Table[v[n + 1]/v[n], {n, 1, z}] (* A203676 *)
A367670
a(n) = Product_{i=1..n, j=1..n} (i^8 + i^4*j^4 + j^8).
Original entry on oeis.org
3, 171714816, 9817265089769041882465383168, 351690857158733335833718073682368165890982417955022627663773696
Offset: 1
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Table[Product[Product[i^8 + i^4*j^4 + j^8, {i, 1, n}], {j, 1, n}], {n, 1, 7}]
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from math import prod, factorial
def A367670(n): return (prod((k:=j**4)**2+(m:=i**4)*(m+k) for i in range(1,n) for j in range(i+1,n+1))*factorial(n)**4)**2*3**n # Chai Wah Wu, Nov 26 2023
A367679
a(n) = Product_{i=1..n, j=1..n} (i^4 - i^3*j + i^2*j^2 - i*j^3 + j^4).
Original entry on oeis.org
1, 1936, 1765124816400, 19271059559619728900751360000, 25048411180596698786915756280274804766474649600000000, 23045227505577134384745253646275782332295626096040088365089618773238077194240000000000
Offset: 1
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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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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
Showing 1-5 of 5 results.
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