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 A318614 #18 Jan 26 2024 15:49:44
%S A318614 1,6,76,1260,24276,515592,11721072,280020312,6945369860,177358000248,
%T A318614 4635276570288,123449340098448,3339525750984528,91535631253610400,
%U A318614 2537277723600799680,71015600640006437040,2004523477053308685540,57003431104378084982040
%N A318614 Scaled g.f. S(u) = Sum_{n>0} a(n)*16*(u/16)^n satisfies T(u) = d/du S(u), with T(u) as defined by A318417; sequence gives a(n).
%C A318614 Area interior to the central loop of u = 2*H = x^2 + y^2 - (1/2)*(x^4 + y^4) equals to Pi*S(u), when u in [0,1/2].
%D A318614 E. Heller, The Semiclassical Way to Dynamics and Spectroscopy, Princeton University Press, 2018, page 204.
%H A318614 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PlaneDivisionbyEllipses.html">Plane Division by Ellipses</a>.
%H A318614 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Circle-EllipseIntersection.html">Circle Ellipse Intersection</a>.
%F A318614 (n-1)^2*n*a(n) - 12*(n-1)*(2*n-3)^2*a(n-1) + 128*(n-2)*(2*n-5)*(2*n-3)*a(n-2) == 0.
%F A318614 a(n) = A000108(n-1)*A098410(n-1).
%e A318614 Singular Value: S(1/2) = 1/sqrt(2).
%e A318614 N=4, h=1/sqrt(2) Quantization: S(u) = (n+1/2)*h/N.
%e A318614 n | u
%e A318614 ==================================================
%e A318614 0 | 0.08544689553344134756293807606337...
%e A318614 1 | 0.23840989875904155311088418238272...
%e A318614 2 | 0.36638282702449450473835851051425...
%e A318614 3 | 0.46595506694324457665483887176081...
%t A318614 RecurrenceTable[{(n-1)^2*n*a[n] - 12*(n-1)*(2*n-3)^2*a[n-1] + 128*(n-2)*(2*n-5)*(2*n-3)*a[n-2] == 0, a[1] == 1, a[2] == 6}, a, {n, 1, 1000}]
%o A318614 (GAP) a:=[1,6];; for n in [3..20] do a[n]:=(1/(n*(n-1)^2))*(12*(n-1)*(2*n-3)^2*a[n-1]-(128*(n-2)*(2*n-5)*(2*n-3)*a[n-2])); od; a; # _Muniru A Asiru_, Sep 24 2018
%Y A318614 Cf. A318417, A010503, A247719, A000888.
%K A318614 nonn
%O A318614 1,2
%A A318614 _Bradley Klee_, Aug 30 2018