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

%I A371998 #6 Apr 25 2024 13:23:21
%S A371998 1,1,0,0,1,3,2,8,9,45,44,264,265,1855,1854,14832,14833,133497,133496,
%T A371998 1334960,1334961,14684571,14684570,176214840,176214841,2290792933,
%U A371998 2290792932,32071101048,32071101049,481066515735,481066515734,7697064251744,7697064251745
%N A371998 a(n) = A000166(floor(n/2)) if n is even otherwise A000240(floor((n + 1)/2)).
%p A371998 a := n -> if irem(n,2) = 0 then A000166(iquo(n,2)) else A000240(iquo(n+1,2)) fi:
%p A371998 seq(a(n), n = 0..32);
%o A371998 (Python)
%o A371998 from functools import cache
%o A371998 @cache
%o A371998 def sf(n):
%o A371998     if n == 0: return 1
%o A371998     return n * sf(n - 1) + (-1 if n % 2 else 1)
%o A371998 def a(n):
%o A371998     h, r = divmod(n, 2)
%o A371998     return sf(h) * (h + 1) if r else sf(h)
%o A371998 print([a(n) for n in range(33)])
%Y A371998 Cf. A000166, A000240.
%K A371998 nonn
%O A371998 0,6
%A A371998 _Peter Luschny_, Apr 25 2024