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Sequence defined by a(2*n) = 2*(n^2 + 2*n) and a(2*n-1) = (2*n)!/n!.
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%I #16 Feb 09 2021 02:30:37

%S 0,2,6,12,16,120,30,1680,48,30240,70,665280,96,17297280,126,518918400,

%T 160,17643225600,198,670442572800,240,28158588057600,286,

%U 1295295050649600,336,64764752532480000,390,3497296636753920000,448

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

%H G. C. Greubel, <a href="/A154030/b154030.txt">Table of n, a(n) for n = 0..700</a>

%F a(2*n) = 2*(n^2 + 2*n).

%F a(2*n-1) = (2*n)!/n!.

%t Flatten[Table[{2*(n^2 - 1), (2*n)!/n!}, {n, 1, 20}]]

%t Table[If[EvenQ[n], 2*((n/2)^2 + n), (n+1)!/((n+1)/2)!], {n, 0, 30}] (* _G. C. Greubel_, Feb 08 2021 *)

%o (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 (Sage)

%o def A154030(n):

%o if (n%2==0): return 2*((n/2)^2 + n)

%o else: return factorial(n+1)/factorial((n+1)/2)

%o [A154030(n) for n in (0..30)] # _G. C. Greubel_, Feb 08 2021

%o (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 Cf. A001813, A054000.

%K nonn,easy

%O 0,2

%A _Roger L. Bagula_, Jan 04 2009

%E Edited by _G. C. Greubel_, Feb 08 2021