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%I #18 Sep 08 2022 08:45:09
%S 1,1,1,1,5,6,7,8,45,60,77,96,585,840,1155,1536,9945,15120,21945,30720,
%T 208845,332640,504735,737280,5221125,8648640,13627845,20643840,
%U 151412625,259459200,422463195,660602880,4996616625,8821612800
%N 4th-order non-linear ("factorial") recursion: a(0)=a(1)=a(2)=a(3)=1, a(n) = (n+1)*a(n-4).
%H Reinhard Zumkeller, <a href="/A081407/b081407.txt">Table of n, a(n) for n = 0..1000</a>
%e Following sequences are interleaved: A007696: {5,45,585,..}; A000404: {6,60,840,..} A034176: {7,77,1155,..}; A034177: {8,96,1536,..}
%t f[n_]:= (n+1)*f[n-4]; f[0]=1; f[1]=1; f[2]=1; f[3]=1; Table[f[n], {n, 0, 40}]
%o (Haskell)
%o a081407 n = a081408_list !! n
%o a081407_list = 1 : 1 : 1 : 1 : zipWith (*) [5..] a081407_list
%o -- _Reinhard Zumkeller_, Jan 05 2012
%o (PARI) a(n) = if(n<4, 1, (n+1)*a(n-4) );
%o vector(35, n, a(n-1)) \\ _G. C. Greubel_, Aug 24 2019
%o (Magma) a:= func< n | n le 3 select 1 else n in [4..6] select n+1 else (n+1)*Self(n-3) >;
%o [a(n): n in [0..35]]; // _G. C. Greubel_, Aug 24 2019
%o (Sage)
%o def a(n):
%o if n<4: return 1
%o elif 4<= n <= 6: return n+1
%o else: return (n+1)*a(n-4)
%o [a(n) for n in (0..35)] # _G. C. Greubel_, Aug 24 2019
%o (GAP)
%o a:= function(k)
%o if k<4 then return 1;
%o elif k<7 then return k+1;
%o else return (k+1)*a(k-4);
%o fi;
%o end;
%o List([0..35], n-> a(n) ); # _G. C. Greubel_, Aug 24 2019
%Y Cf. A000404, A007696, A034176, A034177, A081405, A081405, A081407.
%K nonn
%O 0,5
%A _Labos Elemer_, Apr 01 2003
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