A375446 Triangle read by rows: T(n, k) = n! * 3^k * hypergeom([-k], [-n], -1/3).

1, 1, 2, 2, 5, 13, 6, 16, 43, 116, 24, 66, 182, 503, 1393, 120, 336, 942, 2644, 7429, 20894, 720, 2040, 5784, 16410, 46586, 132329, 376093, 5040, 14400, 41160, 117696, 336678, 963448, 2758015, 7897952, 40320, 115920, 333360, 958920, 2759064, 7940514, 22858094, 65816267, 189550849

Offset: 0

Author

Detlef Meya, Aug 15 2024

Keywords

• nonn
• tabl

Examples

			Triangle starts:
[0] 1,
[1] 1, 2,
[2] 2, 5, 13,
[3] 6, 16, 43, 116,
[4] 24, 66, 182, 503, 1393,
[5] 120, 336, 942, 2644, 7429, 20894,
[6] 720, 2040, 5784, 16410, 46586, 132329, 376093,
[7] 5040, 14400, 41160, 117696, 336678, 963448, 2758015, 7897952,
...
		

Crossrefs

Cf. A375447, A000142, A000180 (diagonal).

Cf. A374427, A374428.

Programs

Mathematica

T[n_, k_] := (-1)^k*Sum[(-3)^(k - j)*Binomial[k, k - j]*(n - j)!, {j, 0, k}];
Table[T[n, k], {n, 0, 8}, {k, 0, n}] // Flatten

Formula

T(n, k) = (-1)^k*Sum_{j=0..k} (-3)^(k - j)*binomial(k, k - j)*(n - j)!.