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 A383439 #14 May 04 2025 03:18:35 %S A383439 1,5,180,10010,678300,51482970,4206302100,361913666400,32356261929420, %T A383439 2979510862285100,280884023785324960,26990111025198348300, %U A383439 2634899457411931245900,260690108634780944767200,26088052554768282442056000,2636591265602354831196585600,268771779551047800167424355500 %N A383439 a(n) = (5*n)!/((n!)^2*(3*n + 1)!). %H A383439 N. J. Wildberger and Dean Rubine, <a href="https://doi.org/10.1080/00029890.2025.2460966">A Hyper-Catalan Series Solution to Polynomial Equations, and the Geode</a>, Amer. Math. Monthly (2025), p. 12. %F A383439 a(n) = A104978(2*n, n), main diagonal of the Bi-Tri array C[m_2, m_3] in the terminology of Wildberger-Rubine. %F A383439 a(n) ~ 4*(20*n - 3)*3^(5/2-3*n)*5^(5*n-1/2)/(n*(25 + 936*n + 2592*n^2)*Pi). - _Stefano Spezia_, May 03 2025 %p A383439 a := n -> (5*n)!/((n!)^2*(3*n + 1)!): %t A383439 Array[(5*#)!/((#!)^2*(3*# + 1)!) &, 17, 0] (* _Michael De Vlieger_, May 03 2025 *) %Y A383439 Cf. A104978, A383440. %K A383439 nonn %O A383439 0,2 %A A383439 _Peter Luschny_, May 03 2025