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A123151 a(n) = A000124(n)*a(n-3) for n > 2, otherwise n!.

%I A123151 #12 Jul 17 2023 18:21:30
%S A123151 1,1,2,7,11,32,154,319,1184,7084,17864,79328,559636,1643488,8408768,
%T A123151 67715956,225157856,1294950272,11647144432,43005150496,273234507392,
%U A123151 2702137508224,10923308225984,75685958547584,813343389975424,3560998481670784,26641457408749568
%N A123151 a(n) = A000124(n)*a(n-3) for n > 2, otherwise n!.
%H A123151 G. C. Greubel, <a href="/A123151/b123151.txt">Table of n, a(n) for n = 0..500</a>
%F A123151 a(n) = n! for n < 3, otherwise a(n) = A000124(n)*a(n-3), where A000124(n) = (n^2 + n + 2)/2.
%t A123151 a[n_]:= a[n]= If[n<3, n!, (1/2)*(n^2+n+2)*a[n-3]];
%t A123151 Table[a[n], {n,0,30}]
%o A123151 (Magma)
%o A123151 function a(n) // a = A123151
%o A123151   if n le 2 then return Factorial(n);
%o A123151   else return (n^2+n+2)*a(n-3)/2;
%o A123151   end if;
%o A123151 end function;
%o A123151 [a(n): n in [0..30]]; // _G. C. Greubel_, Jul 17 2023
%o A123151 (SageMath)
%o A123151 @CachedFunction # a = A123151
%o A123151 def a(n): return factorial(n) if (n<3) else (n^2+n+2)*a(n-3)/2
%o A123151 [a(n) for n in (0..30)] # _G. C. Greubel_, Jul 17 2023
%Y A123151 Cf. A000124, A123150.
%K A123151 nonn,easy
%O A123151 0,3
%A A123151 _Roger L. Bagula_, Oct 01 2006
%E A123151 Edited by _N. J. A. Sloane_, Oct 04 2006
%E A123151 Edited by _G. C. Greubel_, Jul 17 2023