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A081407 4th-order non-linear ("factorial") recursion: a(0)=a(1)=a(2)=a(3)=1, a(n) = (n+1)*a(n-4).

%I A081407 #20 Jan 13 2025 19:52:45
%S A081407 1,1,1,1,5,6,7,8,45,60,77,96,585,840,1155,1536,9945,15120,21945,30720,
%T A081407 208845,332640,504735,737280,5221125,8648640,13627845,20643840,
%U A081407 151412625,259459200,422463195,660602880,4996616625,8821612800
%N A081407 4th-order non-linear ("factorial") recursion: a(0)=a(1)=a(2)=a(3)=1, a(n) = (n+1)*a(n-4).
%H A081407 Reinhard Zumkeller, <a href="/A081407/b081407.txt">Table of n, a(n) for n = 0..1000</a>
%e A081407 Following sequences are interleaved: A007696: {5,45,585,..}; A000404: {6,60,840,..} A034176: {7,77,1155,..}; A034177: {8,96,1536,..}
%t A081407 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}]
%t A081407 nxt[{n_,a_,b_,c_,d_}]:={n+1,b,c,d,a(n+2)}; NestList[nxt,{3,1,1,1,1},40][[;;,2]] (* _Harvey P. Dale_, Jan 13 2025 *)
%o A081407 (Haskell)
%o A081407 a081407 n = a081408_list !! n
%o A081407 a081407_list = 1 : 1 : 1 : 1 : zipWith (*) [5..] a081407_list
%o A081407 -- _Reinhard Zumkeller_, Jan 05 2012
%o A081407 (PARI) a(n) = if(n<4, 1, (n+1)*a(n-4) );
%o A081407 vector(35, n, a(n-1)) \\ _G. C. Greubel_, Aug 24 2019
%o A081407 (Magma) a:= func< n | n le 3 select 1 else n in [4..6] select n+1 else (n+1)*Self(n-3) >;
%o A081407 [a(n): n in [0..35]]; // _G. C. Greubel_, Aug 24 2019
%o A081407 (Sage)
%o A081407 def a(n):
%o A081407     if n<4: return 1
%o A081407     elif 4<= n <= 6: return n+1
%o A081407     else: return (n+1)*a(n-4)
%o A081407 [a(n) for n in (0..35)] # _G. C. Greubel_, Aug 24 2019
%o A081407 (GAP)
%o A081407 a:= function(k)
%o A081407     if k<4 then return 1;
%o A081407     elif k<7 then return k+1;
%o A081407     else return (k+1)*a(k-4);
%o A081407     fi;
%o A081407   end;
%o A081407 List([0..35], n-> a(n) ); # _G. C. Greubel_, Aug 24 2019
%Y A081407 Cf. A000404, A007696, A034176, A034177, A081405, A081405, A081407.
%K A081407 nonn
%O A081407 0,5
%A A081407 _Labos Elemer_, Apr 01 2003