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 A367521 #22 Nov 27 2023 15:06:36
%S A367521 1,2,5,30,99,728,2652,21318,81719,690690,2731365,23841480,96282900,
%T A367521 859515920,3524015272,31983672534,132638171391,1219199353190,
%U A367521 5101386767295,47365474641870,199611643133595,1868545312633440,7921007303554800,74650344244967400
%N A367521 a(n) = binomial(A007310(n+1),n+1)/A007310(n+1).
%C A367521 This sequence is related to sequence A006013.
%F A367521 Limit_{n->oo, n even} a(n)/A006013(n) = 2/3.
%F A367521 a(n) = A006013(n) iff n is 0 or odd.
%F A367521 G.f.: 4F3(1/6,1/3,2/3,5/6; 1/4,3/4,3/2; (729*x^2)/16) - (2 * (4F3(-1/6,1/6,1/3,2/3; 1/4,1/2,3/4; (729*x^2)/16) - 1) / 3*x).
%F A367521 E.g.f.: 4F5(1/6,1/3,2/3,5/6; 1/4,1/2,3/4,1,3/2; (729*x^2)/64) + 2 * x * 4F5(5/6,7/6,4/3,5/3; 5/4,3/2,3/2,7/4,2; (729*x^2)/64).
%o A367521 (PARI) f(n) = n\2*6-(-1)^n; \\ A007310
%o A367521 a(n) = my(x=f(n+1)); binomial(x,n+1)/x; \\ _Michel Marcus_, Nov 22 2023
%Y A367521 Cf. A006013, A007310, A367520.
%K A367521 nonn
%O A367521 0,2
%A A367521 _Miko Labalan_, Nov 21 2023