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 A370232 #11 Feb 14 2024 05:42:12
%S A370232 1,1,1,1,9,1,1,36,25,1,1,100,225,49,1,1,225,1225,784,81,1,1,441,4900,
%T A370232 7056,2025,121,1,1,784,15876,44100,27225,4356,169,1,1,1296,44100,
%U A370232 213444,245025,81796,8281,225,1,1,2025,108900,853776,1656369,1002001,207025,14400,289,1
%N A370232 Triangle read by rows. T(n, k) = binomial(n + k, 2*k)^2.
%F A370232 T(n, k) = [z^k] P(n, z) where P(n, z) = Sum_{k=0..n} binomial(n + k, 2*k) * Pochhammer(n - k + c, 2*k) * z^k / (2*k)! and c = 1.
%F A370232 T(n, k) = [z^k] hypergeom([-n, -n, 1 + n, 1 + n], [1/2, 1/2, 1], z/16).
%e A370232 Triangle starts:
%e A370232 [0] 1;
%e A370232 [1] 1, 1;
%e A370232 [2] 1, 9, 1;
%e A370232 [3] 1, 36, 25, 1;
%e A370232 [4] 1, 100, 225, 49, 1;
%e A370232 [5] 1, 225, 1225, 784, 81, 1;
%e A370232 [6] 1, 441, 4900, 7056, 2025, 121, 1;
%e A370232 [7] 1, 784, 15876, 44100, 27225, 4356, 169, 1;
%t A370232 Table[Binomial[n + k, 2*k]^2, {n, 0, 7}, {k, 0, n}] // Flatten
%Y A370232 Shifted bisection of A182878.
%Y A370232 Cf. A370233 (c=2), A188648 (row sums), A188662 (central terms).
%K A370232 nonn,tabl
%O A370232 0,5
%A A370232 _Peter Luschny_, Feb 12 2024