A375600 Triangle read by rows: T(n, k) = n! * 3^k * hypergeom([-k], [-n], 2/3).

1, 1, 5, 2, 8, 34, 6, 22, 82, 314, 24, 84, 296, 1052, 3784, 120, 408, 1392, 4768, 16408, 56792, 720, 2400, 8016, 26832, 90032, 302912, 1022320, 5040, 16560, 54480, 179472, 592080, 1956304, 6474736, 21468848, 40320, 131040, 426240, 1387680, 4521984, 14750112, 48162944, 157438304, 515252608

Offset: 0

Author

Detlef Meya, Aug 20 2024

Keywords

• nonn
• tabl

Examples

			Triangle starts:
[0] 1;
[1] 1, 5;
[2] 2, 8, 34;
[3] 6, 22, 82, 314;
[4] 24, 84, 296, 1052, 3784;
[5] 120, 408, 1392, 4768, 16408, 56792;
[6] 720, 2400, 8016, 26832, 90032, 302912, 1022320;
[7] 5040, 16560, 54480, 179472, 592080, 1956304, 6474736, 21468848;
...
		

Crossrefs

Cf. A375597, A000142, A097817 (main diagonal).

Cf. A374427, A374428, A375446, A375447.

Programs

Mathematica

T[n_, k_] := 2^k*Sum[(3/2)^(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) = 2^k*Sum_{j=0..k} (3/2)^(k - j)*binomial(k, k - j)*(n - j)!.