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A154030 Sequence defined by a(2*n) = 2*(n^2 + 2*n) and a(2*n-1) = (2*n)!/n!.

%I A154030 #16 Feb 09 2021 02:30:37
%S A154030 0,2,6,12,16,120,30,1680,48,30240,70,665280,96,17297280,126,518918400,
%T A154030 160,17643225600,198,670442572800,240,28158588057600,286,
%U A154030 1295295050649600,336,64764752532480000,390,3497296636753920000,448
%N A154030 Sequence defined by a(2*n) = 2*(n^2 + 2*n) and a(2*n-1) = (2*n)!/n!.
%H A154030 G. C. Greubel, <a href="/A154030/b154030.txt">Table of n, a(n) for n = 0..700</a>
%F A154030 a(2*n) = 2*(n^2 + 2*n).
%F A154030 a(2*n-1) = (2*n)!/n!.
%t A154030 Flatten[Table[{2*(n^2 - 1), (2*n)!/n!}, {n, 1, 20}]]
%t A154030 Table[If[EvenQ[n], 2*((n/2)^2 + n), (n+1)!/((n+1)/2)!], {n, 0, 30}] (* _G. C. Greubel_, Feb 08 2021 *)
%o A154030 (PARI) a(n)=if(n%2, (n+1)!/((n+1)/2)!, 2*(n/2)^2 + 2*n) \\ _Charles R Greathouse IV_, Sep 01 2016
%o A154030 (Sage)
%o A154030 def A154030(n):
%o A154030     if (n%2==0): return 2*((n/2)^2 + n)
%o A154030     else: return factorial(n+1)/factorial((n+1)/2)
%o A154030 [A154030(n) for n in (0..30)] # _G. C. Greubel_, Feb 08 2021
%o A154030 (Magma) [ n mod 2 eq 0 select 2*((n/2)^2 + n) else Round(Factorial(n+1)/Gamma((n+3)/2)): n in [0..30]]; // _G. C. Greubel_, Feb 08 2021
%Y A154030 Cf. A001813, A054000.
%K A154030 nonn,easy
%O A154030 0,2
%A A154030 _Roger L. Bagula_, Jan 04 2009
%E A154030 Edited by _G. C. Greubel_, Feb 08 2021