A381883 Triangle read by rows: T(n, k) = binomial(2*n - 1, k).
1, 1, 1, 1, 3, 3, 1, 5, 10, 10, 1, 7, 21, 35, 35, 1, 9, 36, 84, 126, 126, 1, 11, 55, 165, 330, 462, 462, 1, 13, 78, 286, 715, 1287, 1716, 1716, 1, 15, 105, 455, 1365, 3003, 5005, 6435, 6435, 1, 17, 136, 680, 2380, 6188, 12376, 19448, 24310, 24310
Offset: 0
Examples
Triangle starts: [0] 1; [1] 1, 1; [2] 1, 3, 3; [3] 1, 5, 10, 10; [4] 1, 7, 21, 35, 35; [5] 1, 9, 36, 84, 126, 126; [6] 1, 11, 55, 165, 330, 462, 462; [7] 1, 13, 78, 286, 715, 1287, 1716, 1716; [8] 1, 15, 105, 455, 1365, 3003, 5005, 6435, 6435;
Crossrefs
Programs
-
Maple
T := (n, k) -> binomial(2*n - 1, k): seq(seq(T(n, k), k = 0..n), n = 0..9);
-
Mathematica
T[n_,k_]:=Binomial[2n-1,k];Table[T[n,k],{n,0,9},{k,0,n}]//Flatten (* James C. McMahon, Apr 02 2025 *)