OFFSET
0,3
FORMULA
a(n) = n^n*A009545(n) = n^n*Sum_{j=0..floor((n-1)/2)} binomial(n,2*j+1)*(-1)^j.
a(n) = 0 if and only if n == 0 mod 4.
a(4n) = 0.
a(4n+1) = (4n+1)^(4n+1)*(-4)^n.
a(4n+2) = 2*(4n+2)^(4n+2)*(-4)^n.
a(4n+3) = 2*(4n+3)^(4n+3)*(-4)^n.
PROG
(Python)
def A370359(n): return n**n*((0, 1, 2, 2)[n&3]<<((n>>1)&-2))*(-1 if n&4 else 1)
(PARI) a(n) = imag((n + n*I)^n); \\ Michel Marcus, Feb 16 2024
CROSSREFS
KEYWORD
sign
AUTHOR
Chai Wah Wu, Feb 16 2024
STATUS
approved