A375597 Triangle read by rows: T(n, k) = n! * 3^k * hypergeom([-k], [-n], -2/3).

1, 1, 1, 2, 4, 10, 6, 14, 34, 82, 24, 60, 152, 388, 1000, 120, 312, 816, 2144, 5656, 14968, 720, 1920, 5136, 13776, 37040, 99808, 269488, 5040, 13680, 37200, 101328, 276432, 755216, 2066032, 5659120, 40320, 110880, 305280, 841440, 2321664, 6412128, 17725952, 49045792, 135819136

Offset: 0

Author

Detlef Meya, Aug 20 2024

Keywords

• nonn
• tabl

Examples

			Triangle starts:
[0] 1;
[1] 1, 1;
[2] 2, 4, 10;
[3] 6, 14, 34, 82;
[4] 24, 60, 152, 388, 1000;
[5] 120, 312, 816, 2144, 5656, 14968;
[6] 720, 1920, 5136, 13776, 37040, 99808, 269488;
[7] 5040, 13680, 37200, 101328, 276432, 755216, 2066032, 5659120;
...
		

Crossrefs

Cf. A375600, A000142.

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)!.