%I #6 Feb 27 2023 08:10:15
%S 1,12,280,5544,102960,1847560,32449872,561632400,9617286240,
%T 163352435400,2756930576400,46290177201840,773942488394400,
%U 12893881856650704,214163336821292320,3547937446945842720
%N a(n)=(2n+0^n)*C(4n,2n).
%C The aerated sequence gives the central coefficients in number triangle A166335.
%H Richard P. Brent, Hideyuki Ohtsuka, Judy-anne H. Osborn, and Helmut Prodinger, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL19/Brent/brent9.html">Some Binomial Sums Involving Absolute Values</a>, JIS vol 19 (2016) # 16.3.7 (24)
%F D-finite with recurrence (2*n-1)*(n-1)*a(n) -2*(4*n-1)*(4*n-3)*a(n-1)=0. - _R. J. Mathar_, Feb 27 2023
%t Join[{1},Table[(2n)*Binomial[4n,2n],{n,20}]] (* _Harvey P. Dale_, Jan 21 2015 *)
%K easy,nonn
%O 0,2
%A _Paul Barry_, Oct 12 2009