A371996 Triangle read by rows: T(m, n, k) = 1 if k = 0 and T(m, n, k - 1) if k = n; otherwise (-1)^m*(k - n - 1)^m * T(m, n, k - 1) + T(m, n - 1, k) where m = 3.

1, 1, 1, 1, 9, 9, 1, 36, 297, 297, 1, 100, 2997, 24273, 24273, 1, 225, 17397, 493992, 3976209, 3976209, 1, 441, 72522, 5135400, 142632009, 1145032281, 1145032281, 1, 784, 241866, 35368650, 2406225609, 66113123724, 530050022073, 530050022073

Offset: 0

Author

Peter Luschny, Apr 24 2024

Keywords

• nonn
• tabl

Examples

			Triangle read by rows:
[0] 1;
[1] 1,   1;
[2] 1,   9,     9;
[3] 1,  36,   297,     297;
[4] 1, 100,  2997,   24273,     24273;
[5] 1, 225, 17397,  493992,   3976209,    3976209;
[6] 1, 441, 72522, 5135400, 142632009, 1145032281, 1145032281;
		

Crossrefs

Family: A009766 (Catalan's triangle, m=0), A001498 (m=1), A060058 (m=2), this triangle (m=3), A371997 (m=4).

Cf. A216966 (main diagonal).

Programs

Maple

T := proc(m, n, k) option remember; if k = 0 then 1 elif k = n then T(m, n, k-1) else (-1)^m*(k - n - 1)^m * T(m, n, k - 1) + T(m, n - 1, k) fi end:
seq(seq(T(3, n, k), k = 0..n), n = 0..8));