A190152 Triangle of binomial coefficients binomial(3*n-k,3*n-3*k).

1, 1, 1, 1, 10, 1, 1, 28, 35, 1, 1, 55, 210, 84, 1, 1, 91, 715, 924, 165, 1, 1, 136, 1820, 5005, 3003, 286, 1, 1, 190, 3876, 18564, 24310, 8008, 455, 1, 1, 253, 7315, 54264, 125970, 92378, 18564, 680, 1, 1, 325, 12650, 134596, 490314, 646646, 293930, 38760, 969, 1

Offset: 0

Author

Emanuele Munarini, May 05 2011

Keywords

• nonn
• easy
• tabl

Comments

From R. J. Mathar, Mar 15 2013: (Start)

The matrix inverse starts

1;

-1,1;

9,-10,1;

-288,322,-35,1;

22356,-25003,2730,-84,1;

-3428973,3835026,-418825,12936,-165,1;

914976405,-1023326973,111759115,-3452449,44187,-286,1;

... (End)

Examples

			Triangle begins:
  1
  1, 1
  1, 10, 1
  1, 28, 35, 1
  1, 55, 210, 84, 1
  1, 91, 715, 924, 165, 1
  1, 136, 1820, 5005, 3003, 286, 1
  1, 190, 3876, 18564, 24310, 8008, 455, 1
  1, 253, 7315, 54264, 125970, 92378, 18564, 680, 1
  ...
		

Links

• Nathaniel Johnston, Rows n = 0..100, flattened

Crossrefs

Cf. A000447 (first subdiagonal), A053135 (second subdiagonal), A060544 (second column), A190088, A190153 (row sums), A190154 (diagonal sums).

Programs

Mathematica

Flatten[Table[Binomial[3n - k, 3n - 3k], {n, 0, 9}, {k, 0, n}]]

Maxima

create_list(binomial(3*n-k,3*n-3*k),n,0,9,k,0,n);

PARI

for(n=0,10, for(k=0,n, print1(binomial(3*n-k, 3*(n-k)), ", "))) \\ G. C. Greubel, Dec 29 2017