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

0, 2, 6, 12, 16, 120, 30, 1680, 48, 30240, 70, 665280, 96, 17297280, 126, 518918400, 160, 17643225600, 198, 670442572800, 240, 28158588057600, 286, 1295295050649600, 336, 64764752532480000, 390, 3497296636753920000, 448

Offset: 0

Author

Roger L. Bagula, Jan 04 2009

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..700

Crossrefs

Cf. A001813, A054000.

Programs

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

Mathematica

Flatten[Table[{2*(n^2 - 1), (2*n)!/n!}, {n, 1, 20}]]
Table[If[EvenQ[n], 2*((n/2)^2 + n), (n+1)!/((n+1)/2)!], {n, 0, 30}] (* G. C. Greubel, Feb 08 2021 *)

PARI

a(n)=if(n%2, (n+1)!/((n+1)/2)!, 2*(n/2)^2 + 2*n) \\ Charles R Greathouse IV, Sep 01 2016

Sage

def A154030(n):
    if (n%2==0): return 2*((n/2)^2 + n)
    else: return factorial(n+1)/factorial((n+1)/2)
[A154030(n) for n in (0..30)] # G. C. Greubel, Feb 08 2021

Formula

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

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

Extensions

Edited by G. C. Greubel, Feb 08 2021