A096130 Triangle read by rows: T(n,k) = binomial(k*n,n), 1 <= k <= n.

1, 1, 6, 1, 20, 84, 1, 70, 495, 1820, 1, 252, 3003, 15504, 53130, 1, 924, 18564, 134596, 593775, 1947792, 1, 3432, 116280, 1184040, 6724520, 26978328, 85900584, 1, 12870, 735471, 10518300, 76904685, 377348994, 1420494075, 4426165368, 1, 48620, 4686825, 94143280, 886163135, 5317936260, 23667689815, 85113005120, 260887834350

Offset: 1

Author

Amarnath Murthy, Jul 04 2004

Keywords

• nonn
• tabl

Examples

			Triangle begins:
  1;
  1,   6;
  1,  20,   84;
  1,  70,  495,  1820;
  1, 252, 3003, 15504, 53130;
  ...
		

Links

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

Crossrefs

Row-sums give A096131. The leading diagonal is A014062. Cf. A096131.

Cf. A007318.

Programs

GAP

Flat(List([1..10],n->List([1..n],k->Binomial(k*n,n)))); # Muniru A Asiru, Aug 12 2018

Maple

a:=(n,k)->binomial(k*n,n): seq(seq(a(n,k),k=1..n),n=1..10); # Muniru A Asiru, Aug 12 2018

PARI

tabl(nrows) = {for (n=1, nrows, for (k=1, n, print1(binomial(k*n, n), ", ");); print(););} \\ Michel Marcus, May 14 2013

Formula

T(n, 1) = 1;

T(n, 2) = A000984(n) for n > 1;

T(n, 3) = A005809(n) for n > 2;

T(n, 4) = A005810(n) for n > 3;

T(n, n) = A014062(n).

Extensions

Corrected and extended by Reinhard Zumkeller, Jan 09 2005