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 A383452 #17 May 09 2025 02:36:35 %S A383452 0,0,0,12,165,1430,10010,61880,352716,1899240,9806280,49031400, %T A383452 239028075,1141710570,5362579950,24837212400,113678010600, %U A383452 515030986800,2312957340720,10307744670600,45626928615450,200758485907980,878623171119540,3826892034209552,16596215454480200,71691488703052400,308585103547921200,1323929637802371600 %N A383452 Column 3 in A104978. %H A383452 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 A383452 From _Peter Luschny_, May 04 2025: (Start) %F A383452 a(n) = (3 + 2*n)! / (6*(n - 3)!*(n + 4)!) for n >= 3. %F A383452 a(n) = [x^n] (1/(2*(x*y)^4))*((210*x^4 - 420*x^3 + 252*x^2 - 60*x + 5)/y -(32*x^4 - 176*x^3 + 162*x^2 - 50*x + 5)) where y = sqrt(1 - 4*x). (End) %p A383452 a := n -> ifelse(n < 3, 0, (3 + 2*n)! / (6*(n - 3)!*(n + 4)!)): seq(a(n), n = 0..27); %p A383452 y := sqrt(1 - 4*x): gf := (1/(2*(x*y)^4))*((210*x^4 - 420*x^3 + 252*x^2 - 60*x + 5)/y -(32*x^4 - 176*x^3 + 162*x^2 - 50*x + 5)): ser := series(gf, x, 34): %p A383452 seq(coeff(ser, x, n), n = 0..27); # _Peter Luschny_, May 04 2025 %Y A383452 Cf. A104987. %K A383452 nonn %O A383452 0,4 %A A383452 _N. J. A. Sloane_, May 02 2025