A190088 - OEIS

%I #16 Sep 08 2022 08:45:56

%S 1,1,3,1,15,5,1,36,70,7,1,66,330,210,9,1,105,1001,1716,495,11,1,153,

%T 2380,8008,6435,1001,13,1,210,4845,27132,43758,19448,1820,15,1,276,

%U 8855,74613,203490,184756,50388,3060,17,1,351,14950,177100,735471,1144066,646646,116280,4845,19

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

%C Row sums = A190089.

%C Diagonal sums = A190090.

%H G. C. Greubel, <a href="/A190088/b190088.txt">Table of n, a(n) for the first 100 rows, flattened</a>

%e Triangle begins:

%e 1

%e 1, 3

%e 1, 15, 5

%e 1, 36, 70, 7

%e 1, 66, 330, 210, 9

%e 1, 105, 1001, 1716, 495, 11

%e 1, 153, 2380, 8008, 6435, 1001, 13

%e 1, 210, 4845, 27132, 43758, 19448, 1820, 15

%e 1, 276, 8855, 74613, 203490, 184756, 50388, 3060, 17

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

%o (Maxima) create_list(binomial(3*n-k+1,3*n-3*k+1),n,0,12,k,0,n);

%o (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

%o (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

%Y Cf. A190089, A190090.

%K nonn,easy,tabl

%O 0,3

%A _Emanuele Munarini_, May 04 2011