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
Examples
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
Links
- G. C. Greubel, Table of n, a(n) for the first 100 rows, flattened
Programs
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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
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Mathematica
Flatten[Table[Binomial[3n - k + 1, 3n - 3k + 1], {n, 0, 8}, {k, 0, n}]] -
Maxima
create_list(binomial(3*n-k+1,3*n-3*k+1),n,0,12,k,0,n);
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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
Comments