%I #8 Apr 30 2014 01:36:03
%S 1,2,1,4,6,3,8,24,30,15,16,80,180,210,105,32,240,840,1680,1890,945,64,
%T 672,3360,10080,18900,20790,10395,128,1792,12096,50400,138600,249480,
%U 270270,135135,256,4608,40320,221760,831600,2162160,3783780,4054050
%N Triangular table of 2^n *(n+k)! / ((n-k)! * k! * 4^k).
%F T(n, 0) = A001147(n). T(n, n) = A000079(n).
%e 1; 2, 1; 4, 6, 3; 8, 24, 30, 15; 16, 80, 180, 210, 105; ...
%o (PARI) {T(n, k) = if( k<0 || k>n, 0, 2^n * (n+k)! / ((n-k)! * k! * 4^k))}
%Y Cf. A000079, A001147, A001498, A043301, A043302. Row sums is A043301.
%K nonn,tabl,easy
%O 1,2
%A _Michael Somos_, Jul 16 2002