A371998 a(n) = A000166(floor(n/2)) if n is even otherwise A000240(floor((n + 1)/2)).

1, 1, 0, 0, 1, 3, 2, 8, 9, 45, 44, 264, 265, 1855, 1854, 14832, 14833, 133497, 133496, 1334960, 1334961, 14684571, 14684570, 176214840, 176214841, 2290792933, 2290792932, 32071101048, 32071101049, 481066515735, 481066515734, 7697064251744, 7697064251745

Offset: 0

Author

Peter Luschny, Apr 25 2024

Keywords

• nonn

Crossrefs

Cf. A000166, A000240.

Programs

Maple

a := n -> if irem(n,2) = 0 then A000166(iquo(n,2)) else A000240(iquo(n+1,2)) fi:
seq(a(n), n = 0..32);

Python

from functools import cache
@cache
def sf(n):
    if n == 0: return 1
    return n * sf(n - 1) + (-1 if n % 2 else 1)
def a(n):
    h, r = divmod(n, 2)
    return sf(h) * (h + 1) if r else sf(h)
print([a(n) for n in range(33)])