A361949 Triangle read by rows. T(n, k) = binomial(3*n - 1, 3*k - 1).

1, 10, 1, 28, 56, 1, 55, 462, 165, 1, 91, 2002, 3003, 364, 1, 136, 6188, 24310, 12376, 680, 1, 190, 15504, 125970, 167960, 38760, 1140, 1, 253, 33649, 490314, 1352078, 817190, 100947, 1771, 1, 325, 65780, 1562275, 7726160, 9657700, 3124550, 230230, 2600, 1

Offset: 1

Author

Peter Luschny, Mar 31 2023

Keywords

• nonn
• tabl

Examples

			Table T(n, k) starts:
  [1]   1;
  [2]  10,     1;
  [3]  28,    56,       1;
  [4]  55,   462,     165,       1;
  [5]  91,  2002,    3003,     364,       1;
  [6] 136,  6188,   24310,   12376,     680,       1;
  [7] 190, 15504,  125970,  167960,   38760,    1140,      1;
  [8] 253, 33649,  490314, 1352078,  817190,  100947,   1771,    1;
  [9] 325, 65780, 1562275, 7726160, 9657700, 3124550, 230230, 2600, 1.
		

Crossrefs

Cf. A082365 (row sums), A228888 (subdiagonal), A060544 (column 1), A066802 (central column).

Programs

Maple

T := (n, k) -> binomial(3*n - 1, 3*k - 1):
seq(print(seq(T(n, k), k = 1..n)), n = 1..8);