A253665 a(n) = 2^n*n!/(floor(n/2)!)^2.

1, 2, 8, 48, 96, 960, 1280, 17920, 17920, 322560, 258048, 5677056, 3784704, 98402304, 56229888, 1686896640, 843448320, 28677242880, 12745441280, 484326768640, 193730707456, 8136689713152, 2958796259328, 136104627929088, 45368209309696, 2268410465484800

Offset: 0

Author

Peter Luschny, Feb 01 2015

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A056040, A253666, A098430.

Programs

Maple

a := n -> 2^n*n!/iquo(n,2)!^2: seq(a(n), n=0..25);

Mathematica

Table[2^n*n!/Floor[n/2]!^2, {n, 0, 25}] (* Michael De Vlieger, Feb 02 2015 *)
CoefficientList[Series[(1 + 2 (1 - 8 x) x)/(1 - 16 x^2)^(3/2), {x, 0, 20}],x] (* Benedict W. J. Irwin, Aug 15 2016 *)

PARI

a(n)=2^n*n!/(n\2)!^2 \\ Charles R Greathouse IV, Aug 25 2016

Formula

a(n) = 2^n*A056040(n).

a(2*n) = 4^n*C(2*n, n) = A098430(n).

a(n) = sum(k=0..n, C(n,k)*n!/(floor(n/2)!)^2) = sum(k=0..n, A253666(n,k)).

G.f.: (1+2*(1-8*x)*x)/(1-16*x^2)^(3/2). - Benedict W. J. Irwin, Aug 15 2016