A190152 - OEIS

%I #15 Dec 30 2017 03:30:50

%S 1,1,1,1,10,1,1,28,35,1,1,55,210,84,1,1,91,715,924,165,1,1,136,1820,

%T 5005,3003,286,1,1,190,3876,18564,24310,8008,455,1,1,253,7315,54264,

%U 125970,92378,18564,680,1,1,325,12650,134596,490314,646646,293930,38760,969,1

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

%C From _R. J. Mathar_, Mar 15 2013: (Start)

%C The matrix inverse starts

%C   1;

%C   -1,1;

%C   9,-10,1;

%C   -288,322,-35,1;

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

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

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

%C   ... (End)

%H Nathaniel Johnston, <a href="/A190152/b190152.txt">Rows n = 0..100, flattened</a>

%e Triangle begins:

%e   1

%e   1, 1

%e   1, 10, 1

%e   1, 28, 35, 1

%e   1, 55, 210, 84, 1

%e   1, 91, 715, 924, 165, 1

%e   1, 136, 1820, 5005, 3003, 286, 1

%e   1, 190, 3876, 18564, 24310, 8008, 455, 1

%e   1, 253, 7315, 54264, 125970, 92378, 18564, 680, 1

%e   ...

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

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

%o (PARI) for(n=0,10, for(k=0,n, print1(binomial(3*n-k, 3*(n-k)), ", "))) \\ _G. C. Greubel_, Dec 29 2017

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

%K nonn,easy,tabl

%O 0,5

%A _Emanuele Munarini_, May 05 2011