A342891 - OEIS

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

(list; table; graph; refs; listen; history; text; internal format)

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, 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],

...

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, 12); \\ 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: A176204 A176492 A174731 * A174694 A353952 A340432

Adjacent sequences: A342888 A342889 A342890 * A342892 A342893 A342894

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane, Apr 01 2021

STATUS

approved