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 A381846 #14 May 11 2025 18:00:27
%S A381846 0,0,6,180,4914,142926,4547796,157355484,5842280730,229795151586,
%T A381846 9475645552620,406294220860710,18000809380947036,820011973477512900,
%U A381846 38258534425043501640,1822437060664227775020,88405827105467677196970,4358079981772447955690490,217935769988152202470568700
%N A381846 Area of the unique primitive Pythagorean triple (a,b,c) such that (a-b+c)/2 = A000108(n) and its long leg and hypotenuse are consecutive natural numbers.
%D A381846 Miguel Ángel Pérez García-Ortega, José Manuel Sánchez Muñoz and José Miguel Blanco Casado, El Libro de las Ternas Pitagóricas, Preprint 2025.
%H A381846 Miguel-Ángel Pérez García-Ortega, <a href="/A381846/a381846.pdf">El Libro de las Ternas Pitagóricas</a>
%F A381846 a(n) = (A383615(n,1) * A383615(n,2))/2.
%F A381846 a(n) = (2n)!/(n!(n+1)!)*((2n)!/(n!(n+1)!) - 1)*(2*(2n)!/(n!(n+1)!) - 1).
%e A381846 For n=3, the short leg is A383615(3,1) = 3 and the long leg is A383615(3,2) = 4 so the area is then a(4) = (3 * 4)/2 = 6.
%t A381846 a=Table[(2n)!/(n!(n+1)!),{n,0,18}];Apply[Join,Map[{#(#-1)(2#-1)}&,a]]
%Y A381846 Cf. A000108, A383615, A383616, A131428.
%K A381846 nonn,easy
%O A381846 0,3
%A A381846 _Miguel-Ángel Pérez García-Ortega_, May 06 2025