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A081406 a(n) = (n+1)*a(n-3), a(0)=a(1)=a(2)=1 for n>1.

%I A081406 #16 Sep 08 2022 08:45:09
%S A081406 1,1,1,4,5,6,28,40,54,280,440,648,3640,6160,9720,58240,104720,174960,
%T A081406 1106560,2094400,3674160,24344320,48171200,88179840,608608000,
%U A081406 1252451200,2380855680,17041024000,36321084800,71425670400,528271744000,1162274713600
%N A081406 a(n) = (n+1)*a(n-3), a(0)=a(1)=a(2)=1 for n>1.
%H A081406 Harvey P. Dale, <a href="/A081406/b081406.txt">Table of n, a(n) for n = 0..1000</a>
%e A081406 a(3n+2)=A034001[n]; while other subsequences are near(but not equal) to A001669, A000359.
%t A081406 f[n_]:= (n+1)*f[n-3]; f[0]=1; f[1]=1; f[2]=1; Table[f[n], {n, 30}]
%t A081406 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 A081406 (PARI) a(n) = if(n<3, 1, (n+1)*a(n-3) );
%o A081406 vector(35, n, a(n-1)) \\ _G. C. Greubel_, Aug 24 2019
%o A081406 (Magma) a:= func< n | n le 2 select 1 else n in [3..5] select n+1 else (n+1)*Self(n-2) >;
%o A081406 [a(n): n in [0..35]]; // _G. C. Greubel_, Aug 24 2019
%o A081406 (Sage)
%o A081406 def a(n):
%o A081406     if n<3: return 1
%o A081406     elif 3<= n <= 5: return n+1
%o A081406     else: return (n+1)*a(n-3)
%o A081406 [a(n) for n in (0..35)] # _G. C. Greubel_, Aug 24 2019
%o A081406 (GAP)
%o A081406 a:= function(k)
%o A081406     if k<3 then return 1;
%o A081406     elif k<6 then return k+1;
%o A081406     else return (k+1)*a(k-3);
%o A081406     fi;
%o A081406   end;
%o A081406 List([0..35], n-> a(n) ); # _G. C. Greubel_, Aug 24 2019
%Y A081406 Cf. A002866, A000142, A001147, A081405.
%K A081406 nonn
%O A081406 0,4
%A A081406 _Labos Elemer_, Apr 01 2003
%E A081406 Corrected and extended by _Harvey P. Dale_, Mar 06 2019