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 A279055 #34 Feb 21 2023 11:28:43
%S A279055 1,2,9,80,1240,30240,1071504,51996672,3307723776,266872320000,
%T A279055 26615381760000,3214252921651200,462189467175321600,
%U A279055 78024380924038348800,15279632043682406400000,3435553774431004262400000,879010223384483132866560000,253916900613208108255150080000
%N A279055 Self-convolution of squares of factorial numbers (A001044).
%C A279055 a(n) = (n!)^2 * Sum_{i=0..n} (binomial(n,i)^(-2)).
%C A279055 Consider a triangle ABC with area p. Let points X, Y, Z be randomly and uniformly chosen on sides BC, CA, BA. Let r = area of XYZ. Then the average or expected value of (r/p)^n = a(n)/(n!^2 * (n+1)^3).
%C A279055 a(n) = (3*(n+1)^4 *(n!)^4 /(2n+3)!) * Sum_{i=1..n+1} ((1/i)* binomial(2i, i)), see Sprugnoli Formula 5.2 as noted by Markus Scheuer.
%H A279055 Seiichi Manyama, <a href="/A279055/b279055.txt">Table of n, a(n) for n = 0..253</a>
%H A279055 Arman Maesumi, <a href="https://arxiv.org/abs/1804.11007">Triangle Inscribed-Triangle Picking</a>, arXiv:1804.11007 [math.GM], 2018.
%H A279055 R. Sprugnoli, <a href="http://www.dsi.dsi.unifi.it/~resp/GouldBK.pdf">Riordan Array Proofs of Identities in Gould's Book</a>.
%F A279055 a(n) = Sum_{i=0..n} (i! * (n-i)!)^2.
%F A279055 a(n) ~ 2*(n!)^2. - _Vaclav Kotesovec_, Dec 05 2016
%F A279055 a(n) = A001044(n)*A100516(n)/A100517(n). - _Alois P. Heinz_, Feb 21 2023
%t A279055 Table[Sum[(k!*(n-k)!)^2, {k, 0, n}], {n, 0, 20}] (* _Vaclav Kotesovec_, Dec 05 2016 *)
%Y A279055 Cf. A000142, A001044, A003149, A100516, A100517.
%K A279055 nonn
%O A279055 0,2
%A A279055 _Arman Maesumi_, Dec 04 2016
%E A279055 Definition clarified by _Georg Fischer_, Feb 21 2023