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%I #8 Dec 07 2024 07:42:18
%S 1,3,1,20,15,1,175,189,35,1,1764,2352,720,63,1,19404,29700,12375,1925,
%T 99,1,226512,382239,196625,44044,4212,143,1,2760615,5010005,3006003,
%U 869505,124215,8085,195,1,34763300,66745536,45048640,15767024,2998800,299200,14144,255,1
%N Triangle read by rows: T(n, k) = binomial(2*n+1, n-k)^2*(2*k+1)/(2*n+1)
%F T(n, k) = A034869(2n+1, k) * A039599(n, k).
%e Triangle starts:
%e [0] 1
%e [1] 3, 1
%e [2] 20, 15, 1
%e [3] 175, 189, 35, 1
%e [4] 1764, 2352, 720, 63, 1
%e [5] 19404, 29700, 12375, 1925, 99, 1
%e [6] 226512, 382239, 196625, 44044, 4212, 143, 1
%p T := (n, k) -> binomial(2*n+1, n-k)^2*(2*k+1)/(2*n+1):
%p seq(seq(T(n, k), k = 0..n), n = 0..8); # _Peter Luschny_, Dec 07 2024
%Y First column is A000891.
%Y Cf. A034869, A039599, A002894 (row sums).
%K nonn,tabl,changed
%O 0,2
%A _Henry Bottomley_, Feb 07 2002