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

1, 1, 1, 1, 5, 6, 7, 8, 45, 60, 77, 96, 585, 840, 1155, 1536, 9945, 15120, 21945, 30720, 208845, 332640, 504735, 737280, 5221125, 8648640, 13627845, 20643840, 151412625, 259459200, 422463195, 660602880, 4996616625, 8821612800

Offset

0,5

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

Example

Following sequences are interleaved: A007696: {5,45,585,..}; A000404: {6,60,840,..} A034176: {7,77,1155,..}; A034177: {8,96,1536,..}

Mathematica

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}]
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 *)

Prog

(Haskell)
a081407 n = a081408_list !! n
a081407_list = 1 : 1 : 1 : 1 : zipWith (*) [5..] a081407_list
-- Reinhard Zumkeller, Jan 05 2012
(PARI) a(n) = if(n<4, 1, (n+1)*a(n-4) );
vector(35, n, a(n-1)) \\ G. C. Greubel, Aug 24 2019
(Magma) a:= func< n | n le 3 select 1 else n in [4..6] select n+1 else (n+1)*Self(n-3) >;
[a(n): n in [0..35]]; // G. C. Greubel, Aug 24 2019
(SageMath)
def a(n):
    if n<4: return 1
    elif 4<= n <= 6: return n+1
    else: return (n+1)*a(n-4)
[a(n) for n in (0..35)] # G. C. Greubel, Aug 24 2019
(GAP)
a:= function(k)
    if k<4 then return 1;
    elif k<7 then return k+1;
    else return (k+1)*a(k-4);
    fi;
  end;
List([0..35], n-> a(n) ); # G. C. Greubel, Aug 24 2019

Crossrefs

Cf. A000404, A007696, A034176, A034177, A081405, A081405, A081407.

Sequence in context: A098670 A343570 A320021 * A268857 A205857 A196026

Adjacent sequences: A081404 A081405 A081406 * A081408 A081409 A081410

Keyword

nonn

Author

Labos Elemer, Apr 01 2003

Status

approved