OFFSET
0,3
FORMULA
T(n, k) = Sum_{j=0..k} 3^(k - j)*binomial(k, k - j)*(n - j)!.
EXAMPLE
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;
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
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Detlef Meya, Aug 15 2024
STATUS
approved