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 A383440 #12 May 04 2025 03:19:01 %S A383440 1,16,702,42432,3010700,235282320,19615029280,1712821144320, %T A383440 154870831986156,14388837044278400,1366276815032189060, %U A383440 132069279628944665280,12957831870375876372252,1287484157116598357029120,129316124278441748161584000,13111175417326191857901849600 %N A383440 a(n) = (5*n + 3)!/((8*n^2 + 10*n + 3)*(n!)^2*(3*n + 2)!). %H A383440 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. 17. %F A383440 a(n) = A383453(2*n, n), conjectured by Wildberger-Rubine to be the main diagonal of the Geode Bi-Tri array G[m_2, m_3]. %F A383440 a(n) ~ 3^(-3*n-5/2)*5^(5*n+7/2)/(16*n^2*Pi). - _Stefano Spezia_, May 03 2025 %p A383440 a := n -> ((5*n + 3)!/((8*n^2 + 10*n + 3)*(n!)^2*(3*n + 2)!)): %t A383440 Array[(5*# + 3)!/((8*#^2 + 10*# + 3)*(#!)^2*(3*# + 2)!) &, 16, 0] (* _Michael De Vlieger_, May 03 2025 *) %Y A383440 Cf. A383453, A383439. %K A383440 nonn %O A383440 0,2 %A A383440 _Peter Luschny_, May 03 2025