A342890 Triangle read by rows: T(n,k) = generalized binomial coefficients (n,k)_11 (n >= 0, 0 <= k <= n).

1, 1, 1, 1, 12, 1, 1, 78, 78, 1, 1, 364, 2366, 364, 1, 1, 1365, 41405, 41405, 1365, 1, 1, 4368, 496860, 2318680, 496860, 4368, 1, 1, 12376, 4504864, 78835120, 78835120, 4504864, 12376, 1, 1, 31824, 32821152, 1837984512, 6892441920, 1837984512, 32821152, 31824, 1

Offset

0,5

Comments

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

Links

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

Formula

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

Example

Triangle begins:
  [1],
  [1, 1],
  [1, 12, 1],
  [1, 78, 78, 1],
  [1, 364, 2366, 364, 1],
  [1, 1365, 41405, 41405, 1365, 1],
  [1, 4368, 496860, 2318680, 496860, 4368, 1],
  [1, 12376, 4504864, 78835120, 78835120, 4504864, 12376, 1],
  [1, 31824, 32821152, 1837984512, 6892441920, 1837984512, 32821152, 31824, 1],
...

Prog

(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, 11); \\ Seiichi Manyama, Apr 02 2021

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.

Sequence in context: A174667 A174672 A174151 * A155491 A142460 A156280

Adjacent sequences: A342887 A342888 A342889 * A342891 A342892 A342893

Keyword

nonn,tabl

Author

N. J. A. Sloane, Apr 01 2021

Status

approved