A172479 Triangle read by rows: T(n,k) = A152827(n)/(A152827(k)* A152827(n-k)).

1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 4, 2, 1, 1, 3, 6, 6, 3, 1, 1, 4, 12, 12, 12, 4, 1, 1, 5, 20, 30, 30, 20, 5, 1, 1, 6, 30, 60, 90, 60, 30, 6, 1, 1, 8, 48, 120, 240, 240, 120, 48, 8, 1, 1, 10, 80, 240, 600, 800, 600, 240, 80, 10, 1

Offset: 0

Author

Roger L. Bagula, Feb 04 2010

Keywords

• nonn
• tabl

Comments

Row sums are 1, 2, 3, 6, 10, 20, 46, 112, 284, 834, 2662, ... .

Examples

			Triangle begins:
  1;
  1,   1;
  1,   1,   1;
  1,   2,   2,   1;
  1,   2,   4,   2,   1;
  1,   3,   6,   6,   3,   1;
  1,   4,  12,  12,  12,   4,   1;
  1,   5,  20,  30,  30,  20,   5,   1;
  1,   6,  30,  60,  90,  60,  30,   6,   1;
  1,   8,  48, 120, 240, 240, 120,  48,   8,   1;
  1,  10,  80, 240, 600, 800, 600, 240,  80,  10,   1;
		

Links

• Donald E. Knuth and Herbert S. Wilf, The power of a prime that divides a generalized binomial coefficient, J. Reine Angew. Math., 396:212-219, 1989.

Crossrefs

Cf. A000009, A152827.

Programs

Mathematica

c[n_] := Product[PartitionsQ[m], {m, 1, n}];
t[n_, m_] := c[n]/(c[m]*c[n - m]);
Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]

Formula

T(n,k) = A152827(n)/(A152827(k)* A152827(n-k)).

T(n,k) = Product_{i=1..n} A000009(i)/(Product_{i=1..k} A000009(i)*Product_{i=1..n-k} A000009(i)).

Extensions

New name and edits by Tom Edgar, Jan 23 2015