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 A385669 #13 Aug 04 2025 08:01:48
%S A385669 1,12,184,3088,54216,977712,17946384,333571488,6258363016,
%T A385669 118270099312,2247983617584,42929251009888,823020113236816,
%U A385669 15830699744850912,305362126902698784,5904598544338068288,114417320349085700616,2221310577262416982512
%N A385669 a(n) = Sum_{k=0..n} 2^k * 3^(n-k) * binomial(2*n+1,k) * binomial(2*n-k,n-k).
%F A385669 a(n) = [x^n] (1+2*x)^(2*n+1)/(1-3*x)^(n+1).
%F A385669 a(n) = [x^n] 1/((1-2*x) * (1-5*x)^(n+1)).
%F A385669 a(n) = Sum_{k=0..n} 5^k * (-3)^(n-k) * binomial(2*n+1,k).
%F A385669 a(n) = Sum_{k=0..n} 5^k * 2^(n-k) * binomial(n+k,k).
%o A385669 (PARI) a(n) = sum(k=0, n, 2^k*3^(n-k)*binomial(2*n+1, k)*binomial(2*n-k, n-k));
%Y A385669 Cf. A385670, A385671.
%Y A385669 Cf. A386766.
%K A385669 nonn
%O A385669 0,2
%A A385669 _Seiichi Manyama_, Aug 04 2025