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A324438
a(n) = Product_{i=1..n, j=1..n} (i^5 + j^5).
9
1, 2, 139392, 305013568273920000, 1174837791623127613548781790822400000000, 139642003782073074626249921818187528362524804267528306032640000000000000
OFFSET
0,2
FORMULA
a(n) ~ c * 2^(2*n*(n+1)) * phi^(sqrt(5)*n*(n+1)) * exp(Pi*sqrt(phi)*n*(n+1)/5^(1/4) - 15*n^2/2) * n^(5*n^2 - 5/4), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio and c = 0.1574073828647726237455544898360432469056972905505624900871695...
a(n) = A367679(n) * A079478(n). - Vaclav Kotesovec, Nov 26 2023
For n>0, a(n)/a(n-1) = A272248(n)^2 / (2*n^15). - Vaclav Kotesovec, Dec 02 2023
MAPLE
a:= n-> mul(mul(i^5 + j^5, i=1..n), j=1..n):
seq(a(n), n=0..5); # Alois P. Heinz, Nov 26 2023
MATHEMATICA
Table[Product[i^5 + j^5, {i, 1, n}, {j, 1, n}], {n, 1, 6}]
PROG
(Python)
from math import prod, factorial
def A324438(n): return prod(i**5+j**5 for i in range(1, n) for j in range(i+1, n+1))**2*factorial(n)**5<<n # Chai Wah Wu, Nov 26 2023
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Feb 28 2019
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Nov 26 2023
STATUS
approved