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Triangle: T(n,k)=C(4n-1,2k), 0<=k<=n.
3

%I #5 Mar 30 2012 18:57:38

%S 1,1,3,1,21,35,1,55,330,462,1,105,1365,5005,6435,1,171,3876,27132,

%T 75582,92378,1,253,8855,100947,490314,1144066,1352078,1,351,17550,

%U 296010,2220075,8436285,17383860,20058300,1,465,31465,736281,7888725

%N Triangle: T(n,k)=C(4n-1,2k), 0<=k<=n.

%F T(n,k)=C(4n-1,2k), 0<=k<=n.

%e First 5 rows of A193632:

%e 1

%e 1....3

%e 1....24....44

%e 1....79....878....1434

%e 1....184...6588...50947...77965

%t p[n_, k_] := Binomial[4 n - 1, 2 k];

%t Table[p[n, k], {n, 0, 8}, {k, 0, n}] (* A193632 *)

%t Flatten[%]

%Y Cf. A193633.

%K nonn,tabl

%O 0,3

%A _Clark Kimberling_, Aug 01 2011