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a(n) = (n+1)*a(n-5), with a(0)=a(1)=a(2)=a(3)=a(4)=1.
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%I #19 Sep 08 2022 08:45:09

%S 1,1,1,1,1,6,7,8,9,10,66,84,104,126,150,1056,1428,1872,2394,3000,

%T 22176,31416,43056,57456,75000,576576,848232,1205568,1666224,2250000,

%U 17873856,27143424,39783744,56651616,78750000,643458816,1004306688,1511782272

%N a(n) = (n+1)*a(n-5), with a(0)=a(1)=a(2)=a(3)=a(4)=1.

%C Quintic factorial sequences are generated by single 5-order recursion and appear in unified form.

%H Reinhard Zumkeller, <a href="/A081408/b081408.txt">Table of n, a(n) for n = 0..1000</a>

%e A008548, A034323, A034300, A034301, A034325 sequences are combed together as A081408(5n+r) with r=0,1,2,3,4.

%t a[0]=a[1]=a[2]=a[3]=a[4]=1; a[x_]:= (x+1)*a[x-5]; Table[a[n], {n, 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) m=30; v=concat([1,1,1,1,1], vector(m-5)); for(n=6, m, v[n]=n*v[n-5] ); v \\ _G. C. Greubel_, Aug 15 2019

%o (Magma) [n le 5 select 1 else n*Self(n-5): n in [1..40]]; // _G. C. Greubel_, Aug 15 2019

%o (Sage) def a(n):

%o if (n<5): return 1

%o else: return (n+1)*a(n-5)

%o [a(n) for n in (0..40)] # _G. C. Greubel_, Aug 15 2019

%o (GAP) a:=[1,1,1,1,1];; for n in [6..40] do a[n]:=n*a[n-5]; od; a; # _G. C. Greubel_, Aug 15 2019

%Y Cf. A001147, A002866, A034001, A007599, A034000, A007696, A000407, A034176, A034177, A008548, A034323, A034300, A034301, A034325 [double, triple, quartic, quintic, factorial subsequences], generated together in A081405-A081408.

%K nonn

%O 0,6

%A _Labos Elemer_, Apr 01 2003