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 A336291 #14 Jun 16 2025 18:13:28
%S A336291 0,1,6,39,424,7905,227766,9324511,512970144,36452217969,3247711402870,
%T A336291 354391640998791,46474986465907176,7210874466760191409,
%U A336291 1306387103147257800774,273269900360634449732895,65363179181419926246184576,17726298367452515070739268001
%N A336291 a(n) = (n!)^2 * Sum_{k=1..n} 1 / (k * ((n-k)!)^2).
%F A336291 Sum_{n>=0} a(n) * x^n / (n!)^2 = -log(1 - x) * BesselI(0,2*sqrt(x)).
%F A336291 a(n) ~ BesselI(0,2) * (n!)^2 / n. - _Vaclav Kotesovec_, Jul 17 2020
%F A336291 a(n) = Sum_{k=1..n} (k-1)!*k!*binomial(n,k)^2. - _Ridouane Oudra_, Jun 15 2025
%t A336291 Table[(n!)^2 Sum[1/(k ((n - k)!)^2), {k, 1, n}], {n, 0, 17}]
%t A336291 nmax = 17; CoefficientList[Series[-Log[1 - x] BesselI[0, 2 Sqrt[x]], {x, 0, nmax}], x] Range[0, nmax]!^2
%o A336291 (PARI) a(n) = (n!)^2 * sum(k=1, n, 1 / (k * ((n-k)!)^2)); \\ _Michel Marcus_, Jul 17 2020
%Y A336291 Cf. A002104, A002720, A006040, A336292.
%K A336291 nonn
%O A336291 0,3
%A A336291 _Ilya Gutkovskiy_, Jul 16 2020