cp's OEIS Frontend

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

%I A253665 #19 Aug 26 2016 12:34:04
%S A253665 1,2,8,48,96,960,1280,17920,17920,322560,258048,5677056,3784704,
%T A253665 98402304,56229888,1686896640,843448320,28677242880,12745441280,
%U A253665 484326768640,193730707456,8136689713152,2958796259328,136104627929088,45368209309696,2268410465484800
%N A253665 a(n) = 2^n*n!/(floor(n/2)!)^2.
%H A253665 G. C. Greubel, <a href="/A253665/b253665.txt">Table of n, a(n) for n = 0..500</a>
%F A253665 a(n) = 2^n*A056040(n).
%F A253665 a(2*n) = 4^n*C(2*n, n) = A098430(n).
%F A253665 a(n) = sum(k=0..n, C(n,k)*n!/(floor(n/2)!)^2) = sum(k=0..n, A253666(n,k)).
%F A253665 G.f.: (1+2*(1-8*x)*x)/(1-16*x^2)^(3/2). - _Benedict W. J. Irwin_, Aug 15 2016
%p A253665 a := n -> 2^n*n!/iquo(n,2)!^2: seq(a(n), n=0..25);
%t A253665 Table[2^n*n!/Floor[n/2]!^2, {n, 0, 25}] (* _Michael De Vlieger_, Feb 02 2015 *)
%t A253665 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 *)
%o A253665 (PARI) a(n)=2^n*n!/(n\2)!^2 \\ _Charles R Greathouse IV_, Aug 25 2016
%Y A253665 Cf. A056040, A253666, A098430.
%K A253665 nonn
%O A253665 0,2
%A A253665 _Peter Luschny_, Feb 01 2015