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 A183757 #14 Jul 27 2021 06:02:04 %S A183757 1,1,2,6,17,74,324,1558,7640,38245 %N A183757 Unlabeled super-Catalan numbers: patterns of nonintersecting chords joining unlabeled points on a circle. %C A183757 Interpret the super-Catalan sequence (A001003) as follows: Ways to insert parentheses in a string of n+1 symbols. The parentheses must be balanced but there is no restriction on the number of pairs of parentheses. The number of letters inside a pair of parentheses must be at least 2. Parentheses enclosing the whole string are ignored. Now picture the x's and parentheses as equally spaced unlabeled points on a circle with chords joining paired parentheses and x's having no chord. Circles thus produced may have n+1, n+3, ..., 3*n-1 points and up to n-1 chords. The circle may be rotated. a(n) is the count of unique patterns. %e A183757 super-Catalan(3) = 11: (xx)xx, x(xx)x, xx(xx), (xx)(xx), (xxx)x, x(xxx),((xx)x)x, (x(xx))x, x((xx)x), x(x(xx)), xxxx. This sequence counts unique patterns up to rotation so a(3) = 6: (xx)xx, (xx)(xx), (xxx)x, ((xx)x)x, x(x(xx)), xxxx. %Y A183757 Cf. A001003 super-Catalan numbers. A183758 similar but with reflections discounted. A183759 this sequence decomposed by number of chords in the circles. %K A183757 nonn,more %O A183757 0,3 %A A183757 _David Scambler_, Jan 06 2011