A360546 - OEIS

%I #22 Feb 12 2023 04:53:44

%S 1,5,2,28,20,3,165,168,50,4,1001,1320,588,100,5,6188,10010,5940,1568,

%T 175,6,38760,74256,55055,19800,3528,280,7,245157,542640,482664,220220,

%U 54450,7056,420,8,1562275,3922512,4069800,2252432,715715,130680,12936,600,9

%N 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 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 Triangle begins:

%e      1;

%e      5,     2;

%e     28,    20,    3;

%e    165,   168,   50,    4;

%e   1001,  1320,  588,  100,   5;

%e   6188, 10010, 5940, 1568, 175, 6;

%p A360546 := proc(n, k) m := n-k+1; (1/3)*binomial(3*m, m)*binomial(m + n, k) end:

%p seq(print(seq(A360546(n, k), k = 0..n)), n = 0..8); # _Peter Luschny_, Feb 11 2023

%o (Maxima)

%o 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 Cf. A025174, A134481.

%K nonn,tabl

%O 0,2

%A _Vladimir Kruchinin_, Feb 11 2023