This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A367178 #7 Nov 07 2023 14:43:04 %S A367178 1,1,1,1,4,2,1,9,18,5,1,16,72,80,14,1,25,200,500,350,42,1,36,450,2000, %T A367178 3150,1512,132,1,49,882,6125,17150,18522,6468,429,1,64,1568,15680, %U A367178 68600,131712,103488,27456,1430,1,81,2592,35280,222264,666792,931392,555984,115830,4862 %N A367178 Triangle read by rows. T(n, k) = binomial(n, k)^2 * CatalanNumber(k). %F A367178 T(n, k) = binomial(n, k)^2 * binomial(2*k, k) / (k + 1). %F A367178 T(n, k) = [x^n] hypergeom([1/2, -n, -n], [1, 2], 4*x). %e A367178 Triangle T(n, k) starts: %e A367178 [0] 1; %e A367178 [1] 1, 1; %e A367178 [2] 1, 4, 2; %e A367178 [3] 1, 9, 18, 5; %e A367178 [4] 1, 16, 72, 80, 14; %e A367178 [5] 1, 25, 200, 500, 350, 42; %e A367178 [6] 1, 36, 450, 2000, 3150, 1512, 132; %e A367178 [7] 1, 49, 882, 6125, 17150, 18522, 6468, 429; %e A367178 [8] 1, 64, 1568, 15680, 68600, 131712, 103488, 27456, 1430; %e A367178 [9] 1, 81, 2592, 35280, 222264, 666792, 931392, 555984, 115830, 4862; %p A367178 T := (n, k) -> binomial(n, k)^2 * binomial(2*k, k) / (k + 1): %p A367178 seq(seq(T(n, k), k = 0..n), n = 0..9); %Y A367178 Cf. A086618 (row sums), A186415 (central column), A000108 (main diagonal). %Y A367178 Cf. A098474, A367022, A367023, A387024, A387024, A367177. %K A367178 nonn,tabl %O A367178 0,5 %A A367178 _Peter Luschny_, Nov 07 2023