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 A367520 #25 Nov 27 2023 15:06:43
%S A367520 1,1,3,15,55,364,1428,10659,43263,345345,1430715,11920740,50067108,
%T A367520 429757960,1822766520,15991836267,68328754959,609599676595,
%U A367520 2619631042665,23682737320935,102240109897695,934272656316720,4048514844039120,37325172122483700
%N A367520 a(n) = binomial(A007310(n+1),n)/A007310(n+1).
%C A367520 This sequence is related to sequence A001764.
%F A367520 Limit_{n->oo, n odd} A001764(n)/a(n) = 2/3.
%F A367520 a(n) = A001764(n) iff n is 1 or even.
%F A367520 G.f.: ((1 - 4F3(-1/6,1/6,1/3,2/3; 1/4,1/2,3/4; (729*x^2)/16)) / 3*x) + 4F3(1/6,1/3,2/3,5/6; 1/2,3/4,5/4; (729*x^2)/16).
%F A367520 E.g.f.: 4F5(1/6,1/3,2/3,5/6; 1/2,1/2,3/4,1,5/4; (729*x^2)/64) + x * 4F5(5/6,7/6,4/3,5/3; 5/4,3/2,3/2,7/4,2; (729*x^2)/64).
%o A367520 (PARI) f(n) = n\2*6-(-1)^n; \\ A007310
%o A367520 a(n) = my(x=f(n+1)); binomial(x,n)/x; \\ _Michel Marcus_, Nov 22 2023
%Y A367520 Cf. A001764, A007310, A235534, A367521.
%K A367520 nonn
%O A367520 0,3
%A A367520 _Miko Labalan_, Nov 21 2023