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 A383776 #26 May 15 2025 17:09:09 %S A383776 6,16,53,186,672,2472,9207,34606,130988,498576,1906346,7316596, %T A383776 28170768,108760560,420889995,1632155670,6340808820,24673450560, %U A383776 96148670310,375164728620,1465589068320,5731488987120,22436098732710,87905595401676,344702077523352,1352701532137312,5312100899224532,20874451526714856 %N A383776 a(n) = (11*n + 3 + 6/(n+2)) * Catalan(n). %C A383776 It appears that for n >= 2 a(n-2) is the number of lattice points in the n-dimensional lattice polytope defined, in the space with coordinates (x_1,x_2,...,x_n), by the equations x_i >= 0 for every i, sum_i x_i <= n and x_1 + x_2 <= 2. For n=2, this is a triangle with 6 lattice points. %H A383776 Paolo Xausa, <a href="/A383776/b383776.txt">Table of n, a(n) for n = 0..1000</a> %F A383776 a(n) = (11*n + 3 + 6/(n + 2))*Catalan(n). %F A383776 G.f.: 2*(7 + 5*sqrt(1 - 4*x) - 6*x)/((1 + sqrt(1 - 4*x))^2*sqrt(1 - 4*x)). - _Stefano Spezia_, May 15 2025 %t A383776 A383776[n_] := (11*n + 3 + 6/(n + 2))*CatalanNumber[n]; %t A383776 Array[A383776, 30, 0] (* _Paolo Xausa_, May 15 2025 *) %o A383776 (Sage) %o A383776 [(11*n+3+6/(n+2))*catalan_number(n) for n in range(12)] %Y A383776 Cf. A000108, A000984, A007054, A051960. %K A383776 nonn,easy %O A383776 0,1 %A A383776 _F. Chapoton_, May 09 2025