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A360546 Triangle read by rows: T(n, m) = (n+1-m)*C(2*n+2-m, m)*C(3*n-3*m+2, n-m+1)/(2*n-m+2).

%I A360546 #22 Feb 12 2023 04:53:44
%S A360546 1,5,2,28,20,3,165,168,50,4,1001,1320,588,100,5,6188,10010,5940,1568,
%T A360546 175,6,38760,74256,55055,19800,3528,280,7,245157,542640,482664,220220,
%U A360546 54450,7056,420,8,1562275,3922512,4069800,2252432,715715,130680,12936,600,9
%N A360546 Triangle read by rows: T(n, m) = (n+1-m)*C(2*n+2-m, m)*C(3*n-3*m+2, n-m+1)/(2*n-m+2).
%F A360546 G.f.: -1/(2*x) + (sqrt(3)*cot((1/3)*arcsin((3*sqrt(3)*sqrt(x))/(2- 2*x*y))))/ (2*sqrt(x*(-27*x + 4*(-1+x*y)^2))).
%e A360546 Triangle begins:
%e A360546      1;
%e A360546      5,     2;
%e A360546     28,    20,    3;
%e A360546    165,   168,   50,    4;
%e A360546   1001,  1320,  588,  100,   5;
%e A360546   6188, 10010, 5940, 1568, 175, 6;
%p A360546 A360546 := proc(n, k) m := n-k+1; (1/3)*binomial(3*m, m)*binomial(m + n, k) end:
%p A360546 seq(print(seq(A360546(n, k), k = 0..n)), n = 0..8); # _Peter Luschny_, Feb 11 2023
%o A360546 (Maxima)
%o A360546 T(n,m):=if n<m then 0 else ((n+1-m)*binomial(2*n+2-m,m)*binomial(3*n-3*m+2,n-m+1))/(2*n-m+2);
%Y A360546 Cf. A025174, A134481.
%K A360546 nonn,tabl
%O A360546 0,2
%A A360546 _Vladimir Kruchinin_, Feb 11 2023