A342891 Triangle read by rows: T(n,k) = generalized binomial coefficients (n,k)_12 (n >= 0, 0 <= k <= n).

1, 1, 1, 1, 13, 1, 1, 91, 91, 1, 1, 455, 3185, 455, 1, 1, 1820, 63700, 63700, 1820, 1, 1, 6188, 866320, 4331600, 866320, 6188, 1, 1, 18564, 8836464, 176729280, 176729280, 8836464, 18564, 1, 1, 50388, 71954064, 4892876352, 19571505408, 4892876352, 71954064, 50388, 1

Offset: 0

Author

N. J. A. Sloane, Apr 01 2021

Keywords

• nonn
• tabl

Comments

For references, links, programs, etc., see earlier sequences in this series, especially A342889.

Examples

			Triangle begins:
  [1],
  [1, 1],
  [1, 13, 1],
  [1, 91, 91, 1],
  [1, 455, 3185, 455, 1],
  [1, 1820, 63700, 63700, 1820, 1],
  [1, 6188, 866320, 4331600, 866320, 6188, 1],
  [1, 18564, 8836464, 176729280, 176729280, 8836464, 18564, 1],
...
		

Links

• Seiichi Manyama, Rows n = 0..139, flattened

Crossrefs

Triangles of generalized binomial coefficients (n,k)_m (or generalized Pascal triangles) for m = 1,...,12: A007318 (Pascal), A001263, A056939, A056940, A056941, A142465, A142467, A142468, A174109, A342889, A342890, A342891.

Programs

PARI

f(n, k, m) = prod(j=1, k, binomial(n-j+m, m)/binomial(j-1+m, m));
T(n, k) = f(n, k, 12); \\ Seiichi Manyama, Apr 02 2021

Formula

The generalized binomial coefficient (n,k)m = Product{j=1..k} binomial(n+m-j,m)/binomial(j+m-1,m).