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A154030 Sequence defined by a(2*n) = 2*(n^2 + 2*n) and a(2*n-1) = (2*n)!/n!. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

FORMULA

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

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

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 *)

PROG

(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

(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

CROSSREFS

Cf. A001813, A054000.

Sequence in context: A130237 A053457 A299112 * A055560 A237719 A108727

Adjacent sequences:  A154027 A154028 A154029 * A154031 A154032 A154033

KEYWORD

nonn,easy

AUTHOR

Roger L. Bagula, Jan 04 2009

EXTENSIONS

Edited by G. C. Greubel, Feb 08 2021

STATUS

approved

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Last modified November 30 05:12 EST 2021. Contains 349419 sequences. (Running on oeis4.)