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

%I A190152 #15 Dec 30 2017 03:30:50
%S A190152 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 A190152 5005,3003,286,1,1,190,3876,18564,24310,8008,455,1,1,253,7315,54264,
%U A190152 125970,92378,18564,680,1,1,325,12650,134596,490314,646646,293930,38760,969,1
%N A190152 Triangle of binomial coefficients binomial(3*n-k,3*n-3*k).
%C A190152 From _R. J. Mathar_, Mar 15 2013: (Start)
%C A190152 The matrix inverse starts
%C A190152   1;
%C A190152   -1,1;
%C A190152   9,-10,1;
%C A190152   -288,322,-35,1;
%C A190152   22356,-25003,2730,-84,1;
%C A190152   -3428973,3835026,-418825,12936,-165,1;
%C A190152   914976405,-1023326973,111759115,-3452449,44187,-286,1;
%C A190152   ... (End)
%H A190152 Nathaniel Johnston, <a href="/A190152/b190152.txt">Rows n = 0..100, flattened</a>
%e A190152 Triangle begins:
%e A190152   1
%e A190152   1, 1
%e A190152   1, 10, 1
%e A190152   1, 28, 35, 1
%e A190152   1, 55, 210, 84, 1
%e A190152   1, 91, 715, 924, 165, 1
%e A190152   1, 136, 1820, 5005, 3003, 286, 1
%e A190152   1, 190, 3876, 18564, 24310, 8008, 455, 1
%e A190152   1, 253, 7315, 54264, 125970, 92378, 18564, 680, 1
%e A190152   ...
%t A190152 Flatten[Table[Binomial[3n - k, 3n - 3k], {n, 0, 9}, {k, 0, n}]]
%o A190152 (Maxima) create_list(binomial(3*n-k,3*n-3*k),n,0,9,k,0,n);
%o A190152 (PARI) for(n=0,10, for(k=0,n, print1(binomial(3*n-k, 3*(n-k)), ", "))) \\ _G. C. Greubel_, Dec 29 2017
%Y A190152 Cf. A000447 (first subdiagonal), A053135 (second subdiagonal), A060544 (second column), A190088, A190153 (row sums), A190154 (diagonal sums).
%K A190152 nonn,easy,tabl
%O A190152 0,5
%A A190152 _Emanuele Munarini_, May 05 2011