A190088 Triangle of binomial coefficients binomial(3*n-k+1,3*n-3*k+1).

1, 1, 3, 1, 15, 5, 1, 36, 70, 7, 1, 66, 330, 210, 9, 1, 105, 1001, 1716, 495, 11, 1, 153, 2380, 8008, 6435, 1001, 13, 1, 210, 4845, 27132, 43758, 19448, 1820, 15, 1, 276, 8855, 74613, 203490, 184756, 50388, 3060, 17, 1, 351, 14950, 177100, 735471, 1144066, 646646, 116280, 4845, 19

Offset

0,3

Comments

Row sums = A190089.

Diagonal sums = A190090.

Links

G. C. Greubel, Table of n, a(n) for the first 100 rows, flattened

Example

Triangle begins:
1
1, 3
1, 15, 5
1, 36, 70, 7
1, 66, 330, 210, 9
1, 105, 1001, 1716, 495, 11
1, 153, 2380, 8008, 6435, 1001, 13
1, 210, 4845, 27132, 43758, 19448, 1820, 15
1, 276, 8855, 74613, 203490, 184756, 50388, 3060, 17

Mathematica

Flatten[Table[Binomial[3n - k + 1, 3n - 3k + 1], {n, 0, 8}, {k, 0, n}]]

Prog

(Maxima) create_list(binomial(3*n-k+1, 3*n-3*k+1), n, 0, 12, k, 0, n);
(PARI) for(n=0, 10, for(k=0, n, print1(binomial(3*n-k+1, 3*n-3*k+1), ", "))) \\ G. C. Greubel, Mar 04 2018
(Magma) /* As triangle */ [[Binomial(3*n-k+1, 3*n-3*k+1): k in [0..n]]: n in [0..10]]; // G. C. Greubel, Mar 04 2018

Crossrefs

Cf. A190089, A190090.

Sequence in context: A324428 A131440 A269950 * A119301 A293157 A121335

Adjacent sequences: A190085 A190086 A190087 * A190089 A190090 A190091

Keyword

nonn,easy,tabl

Author

Emanuele Munarini, May 04 2011

Status

approved