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 A367025 #14 Nov 20 2023 11:52:33 %S A367025 1,4,1,9,9,2,16,36,32,5,25,100,200,125,14,36,225,800,1125,504,42,49, %T A367025 441,2450,6125,6174,2058,132,64,784,6272,24500,43904,32928,8448,429, %U A367025 81,1296,14112,79380,222264,296352,171072,34749,1430 %N A367025 Triangle read by rows, T(n, k) = [x^k] p(n), where p(n) = (1 - hypergeom([-1/2, -n - 1, -n - 1], [1, 1], 4*x)) / (2*x). %F A367025 T(n,k) = binomial(n+1,n-k)^2*binomial(2*k,k)/(k+1). - _Detlef Meya_, Nov 19 2023 %e A367025 Triangle T(n, k) starts: %e A367025 [0] 1; %e A367025 [1] 4, 1; %e A367025 [2] 9, 9, 2; %e A367025 [3] 16, 36, 32, 5; %e A367025 [4] 25, 100, 200, 125, 14; %e A367025 [5] 36, 225, 800, 1125, 504, 42; %e A367025 [6] 49, 441, 2450, 6125, 6174, 2058, 132; %e A367025 [7] 64, 784, 6272, 24500, 43904, 32928, 8448, 429; %e A367025 [8] 81, 1296, 14112, 79380, 222264, 296352, 171072, 34749, 1430; %e A367025 [9] 100, 2025, 28800, 220500, 889056, 1852200, 1900800, 868725, 143000, 4862; %p A367025 p := n -> (1 - hypergeom([-1/2, -n-1, -n-1], [1, 1], 4*x)) / (2*x): %p A367025 T := (n, k) -> coeff(simplify(p(n)), x, k): %p A367025 seq(seq(T(n, k), k = 0..n), n = 0..9); %t A367025 T[n_,k_]:=Binomial[n+1,n-k]^2*Binomial[2*k,k]/(k+1);Flatten[Table[T[n,k],{n,0,9},{k,0,n}]] (* _Detlef Meya_, Nov 19 2023 *) %Y A367025 Cf. A000290 (first column), A000108 (main diagonal). %Y A367025 Cf. A367022, A367023, A387024. %K A367025 nonn,tabl %O A367025 0,2 %A A367025 _Peter Luschny_, Nov 07 2023