A371997 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 = 4.

1, 1, 1, 1, 17, 17, 1, 98, 1585, 1585, 1, 354, 30259, 485729, 485729, 1, 979, 280883, 23237252, 372281761, 372281761, 1, 2275, 1702758, 459143300, 37562889061, 601378506737, 601378506737, 1, 4676, 7762854, 5310927050, 1397160213861, 113771355829478, 1820943071778385, 1820943071778385

Offset: 0

Author

Peter Luschny, Apr 24 2024

Keywords

• nonn
• tabl

Examples

			Triangle begins:
[0] 1;
[1] 1,    1;
[2] 1,   17,      17;
[3] 1,   98,    1585,      1585;
[4] 1,  354,   30259,    485729,      485729;
[5] 1,  979,  280883,  23237252,   372281761,    372281761;
[6] 1, 2275, 1702758, 459143300, 37562889061, 601378506737, 601378506737;
		

Crossrefs

Family: A009766 (Catalan's triangle, m=0), A001498 (m=1), A060058 (m=2), A371996 (m=3), this triangle (m=4).

Cf. A227887 (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(4, n, k), k = 0..n), n = 0..8));