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

0,5

Links

Table of n, a(n) for n=0..54.

Example

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;

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 *)

Crossrefs

Cf. A007318 (Pascal), A088218 (main diagonal), A114121 (row sums), A262977 (central terms).

Sequence in context: A193823 A071945 A209583 * A144944 A137426 A269949

Adjacent sequences: A381880 A381881 A381882 * A381884 A381885 A381886

Keyword

nonn,tabl,easy

Author

Peter Luschny, Mar 15 2025

Status

approved