A375447 Triangle read by rows: T(n, k) = n! * 3^k * hypergeom([-k], [-n], 1/3).

1, 1, 4, 2, 7, 25, 6, 20, 67, 226, 24, 78, 254, 829, 2713, 120, 384, 1230, 3944, 12661, 40696, 720, 2280, 7224, 22902, 72650, 230611, 732529, 5040, 15840, 49800, 156624, 492774, 1550972, 4883527, 15383110, 40320, 126000, 393840, 1231320, 3850584, 12044526, 37684550, 117937177, 369194641

Offset: 0

Author

Detlef Meya, Aug 15 2024

Keywords

• nonn
• tabl

Examples

			Triangle starts:
[0] 1;
[1] 1, 4;
[2] 2, 7, 25;
[3] 6, 20, 67, 226;
[4] 24, 78, 254, 829, 2713;
[5] 120, 384, 1230, 3944, 12661, 40696;
[6] 720, 2280, 7224, 22902, 72650, 230611, 732529;
		

Crossrefs

Cf. A375446, A000142, A010845.

Cf. A374427, A374428.

Programs

Mathematica

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