A322127 Triangular array, read by rows: T(n,k) = numerator of binomial(n-1, n-k)/k!, 1 <= k <= n.

1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 1, 5, 5, 5, 1, 1, 1, 3, 5, 5, 1, 1, 1, 1, 7, 7, 35, 7, 7, 1, 1, 1, 4, 14, 7, 7, 7, 1, 1, 1, 1, 9, 6, 7, 21, 7, 1, 1, 1, 1, 1, 5, 15, 5, 7, 7, 1, 1, 1, 1, 1, 1, 11, 55, 55, 11, 77, 11, 11, 11, 11, 1, 1, 1, 6, 11, 55, 33, 11, 11, 11, 11, 11, 1, 1, 1

Offset: 1

Author

Seiichi Manyama, Nov 27 2018

Keywords

• nonn
• frac
• tabl
• look

Examples

			T(n,k) = binomial(n-1, n-k)/k!.
1/1;
1/1, 1/2;
1/1, 1/1, 1/6;
1/1, 3/2, 1/2,  1/24;
1/1, 2/1, 1/1,   1/6, 1/120;
1/1, 5/2, 5/3,  5/12,  1/24, 1/720;
1/1, 3/1, 5/2,   5/6,   1/8, 1/120, 1/5040;
1/1, 7/2, 7/2, 35/24,  7/24, 7/240,  1/720, 1/40320;
		

Links

• Seiichi Manyama, Rows n = 1..140, flattened

Crossrefs

Cf. A007318, A322093, A322128.

Programs

Mathematica

T[n_, k_] := Numerator[Binomial[n-1, n-k]/k!]; Table[T[n, k], {n,1,10}, {k,1,n}] // Flatten (* Amiram Eldar, Nov 27 2018 *)