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a(n) = (n+1)*a(n-3), a(0)=a(1)=a(2)=1 for n>1.
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%I #16 Sep 08 2022 08:45:09

%S 1,1,1,4,5,6,28,40,54,280,440,648,3640,6160,9720,58240,104720,174960,

%T 1106560,2094400,3674160,24344320,48171200,88179840,608608000,

%U 1252451200,2380855680,17041024000,36321084800,71425670400,528271744000,1162274713600

%N a(n) = (n+1)*a(n-3), a(0)=a(1)=a(2)=1 for n>1.

%H Harvey P. Dale, <a href="/A081406/b081406.txt">Table of n, a(n) for n = 0..1000</a>

%e a(3n+2)=A034001[n]; while other subsequences are near(but not equal) to A001669, A000359.

%t f[n_]:= (n+1)*f[n-3]; f[0]=1; f[1]=1; f[2]=1; Table[f[n], {n, 30}]

%t RecurrenceTable[{a[0]==a[1]==a[2]==1,a[n]==(n+1)a[n-3]},a,{n,30}] (* _Harvey P. Dale_, Mar 06 2019 *)

%o (PARI) a(n) = if(n<3, 1, (n+1)*a(n-3) );

%o vector(35, n, a(n-1)) \\ _G. C. Greubel_, Aug 24 2019

%o (Magma) a:= func< n | n le 2 select 1 else n in [3..5] select n+1 else (n+1)*Self(n-2) >;

%o [a(n): n in [0..35]]; // _G. C. Greubel_, Aug 24 2019

%o (Sage)

%o def a(n):

%o if n<3: return 1

%o elif 3<= n <= 5: return n+1

%o else: return (n+1)*a(n-3)

%o [a(n) for n in (0..35)] # _G. C. Greubel_, Aug 24 2019

%o (GAP)

%o a:= function(k)

%o if k<3 then return 1;

%o elif k<6 then return k+1;

%o else return (k+1)*a(k-3);

%o fi;

%o end;

%o List([0..35], n-> a(n) ); # _G. C. Greubel_, Aug 24 2019

%Y Cf. A002866, A000142, A001147, A081405.

%K nonn

%O 0,4

%A _Labos Elemer_, Apr 01 2003

%E Corrected and extended by _Harvey P. Dale_, Mar 06 2019