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 A383451 #9 May 04 2025 08:02:23 %S A383451 5,84,990,10010,92820,813960,6864396,56241900,450675225,3548173200, %T A383451 27536909400,211183061544,1603426948760,12070359895440,90193956545880, %U A383451 669621798598200,4943243777508855,36308086251336900,265483485367681350,1933360478165412450,14028103934595550800,101447684961932268960,731424072912190585200,5258854714114889362800 %N A383451 3nd diagonal (from right) in A104978. %H A383451 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). See table on page 12. %F A383451 From _Peter Luschny_, May 04 2025: (Start) %F A383451 a(n) = (3*n + 6)!/(6*n!*(3 + 2*n + 1)!). %F A383451 a(n) = [x^n] 5*hypergeom([7/3, 8/3], [5/2], (27*x)/4). (End) %p A383451 From _Peter Luschny_, May 04 2025: (Start) %p A383451 a := n -> (3*n + 6)!/(6*n!*(3 + 2*n + 1)!): seq(a(n), n = 0..23); %p A383451 gf := 5*hypergeom([7/3, 8/3], [5/2], (27*x)/4): %p A383451 ser := series(gf, x, 25): seq(coeff(ser, x, k), k = 0..23); (End) %Y A383451 Cf. A104987. %K A383451 nonn %O A383451 0,1 %A A383451 _N. J. A. Sloane_, May 02 2025