OFFSET
1,2
FORMULA
a(n) = A362291(n)*(m!)^2*(n^2 - 2*m)!, where m = 2*floor(n/2).
EXAMPLE
PROG
(Python)
from math import factorial
from itertools import combinations as C
def a(n):
E = [i for i in range(1, n**2+1)]
m = n if n%2 == 0 else n-1
r = n**2 - 2*m
fm, fr = factorial(m), factorial(r)
p = fm**2 * fr
return p*sum(1 for u in C(E, 2*m) for t in C(u, m) if 2*sum(t)==sum(u))
print([a(n) for n in range(1, 5)])
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Stefano Spezia and Michael S. Branicky, Apr 14 2023
EXTENSIONS
a(6)-a(8) calculated from A362291 by Martin Ehrenstein, Apr 25 2023
STATUS
approved