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a(0)=0, a(1)=1, a(n) = n! - a(n-2).
4

%I #16 Oct 01 2024 15:45:10

%S 0,1,2,5,22,115,698,4925,39622,357955,3589178,39558845,475412422,

%T 6187461955,86702878778,1301486906045,20836087009222,354385941189955,

%U 6381537618718778,121290714467642045,2426520470557921222,50969651457241797955,1121574207307049758778

%N a(0)=0, a(1)=1, a(n) = n! - a(n-2).

%F D-finite with recurrence a(n) -n*a(n-1) +a(n-2) -n*a(n-3)=0. - _R. J. Mathar_, Jun 04 2021

%p a:= proc(n) a(n):= `if`(n<2, n, n! - a(n-2)) end:

%p seq(a(n), n=0..23); # _Alois P. Heinz_, Jun 04 2021

%t nxt[{n_,a_,b_}]:={n+1,b,(n+1)!-a}; NestList[nxt,{1,0,1},30][[;;,2]] (* _Harvey P. Dale_, Feb 15 2024 *)

%o (Python)

%o prpr = 0

%o prev = f = 1

%o for n in range(2, 33):

%o print(prpr, end=', ')

%o f *= n

%o curr = f - prpr

%o prpr = prev

%o prev = curr

%Y Cf. A000142.

%Y Cf. A005165: a(0) = 0, a(n) = n! - a(n-1).

%K nonn

%O 0,3

%A _Alex Ratushnyak_, Aug 03 2012