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 A386763 #19 Aug 03 2025 07:47:40
%S A386763 1,8,114,1862,32246,576768,10529544,194960802,3647285766,68772760928,
%T A386763 1304858513324,24882531221292,476462691535436,9155397868559288,
%U A386763 176447193966483204,3409285356643013082,66020593061854488006,1280989373915746600848,24897996624141835608684
%N A386763 a(n) = Sum_{k=0..n} 5^k * 3^(n-k) * binomial(n+k-1,k).
%F A386763 a(n) = Sum_{k=0..n} 3^k * 2^(n-k) * binomial(2*n,k) * binomial(2*n-k-1,n-k).
%F A386763 a(n) = [x^n] ( (1+3*x)^2/(1-2*x) )^n.
%F A386763 The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x * (1-2*x) / (1+3*x)^2 ). See A386769.
%F A386763 a(n) = Sum_{k=0..n} 5^k * (-2)^(n-k) * binomial(2*n,k).
%F A386763 a(n) = (-9/2)^n*(1 - (-10/9)^n*binomial(2*n-1, n)*(hypergeom([1, 2*n], [1+n], 5/3) - 1)). - _Stefano Spezia_, Aug 02 2025
%o A386763 (PARI) a(n) = sum(k=0, n, 5^k*3^(n-k)*binomial(n+k-1, k));
%Y A386763 Cf. A386764, A386765.
%Y A386763 Cf. A383888, A386769.
%K A386763 nonn
%O A386763 0,2
%A A386763 _Seiichi Manyama_, Aug 02 2025