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A081408 a(n) = (n+1)*a(n-5), with a(0)=a(1)=a(2)=a(3)=a(4)=1.

%I A081408 #19 Sep 08 2022 08:45:09
%S A081408 1,1,1,1,1,6,7,8,9,10,66,84,104,126,150,1056,1428,1872,2394,3000,
%T A081408 22176,31416,43056,57456,75000,576576,848232,1205568,1666224,2250000,
%U A081408 17873856,27143424,39783744,56651616,78750000,643458816,1004306688,1511782272
%N A081408 a(n) = (n+1)*a(n-5), with a(0)=a(1)=a(2)=a(3)=a(4)=1.
%C A081408 Quintic factorial sequences are generated by single 5-order recursion and appear in unified form.
%H A081408 Reinhard Zumkeller, <a href="/A081408/b081408.txt">Table of n, a(n) for n = 0..1000</a>
%e A081408 A008548, A034323, A034300, A034301, A034325 sequences are combed together as A081408(5n+r) with r=0,1,2,3,4.
%t A081408 a[0]=a[1]=a[2]=a[3]=a[4]=1; a[x_]:= (x+1)*a[x-5]; Table[a[n], {n, 40}]
%o A081408 (Haskell)
%o A081408 a081407 n = a081408_list !! n
%o A081408 a081407_list = 1 : 1 : 1 : 1 : zipWith (*) [5..] a081407_list
%o A081408 -- _Reinhard Zumkeller_, Jan 05 2012
%o A081408 (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 A081408 (Magma) [n le 5 select 1 else n*Self(n-5): n in [1..40]]; // _G. C. Greubel_, Aug 15 2019
%o A081408 (Sage) def a(n):
%o A081408     if (n<5): return 1
%o A081408     else: return (n+1)*a(n-5)
%o A081408 [a(n) for n in (0..40)] # _G. C. Greubel_, Aug 15 2019
%o A081408 (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 A081408 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 A081408 nonn
%O A081408 0,6
%A A081408 _Labos Elemer_, Apr 01 2003