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 A386941 #20 Aug 12 2025 02:41:46
%S A386941 1,7,45,276,1645,9618,55468,316620,1792989,10089420,56482998,
%T A386941 314859636,1748876220,9684449908,53487036420,294732771280,
%U A386941 1620825793053,8897604701130,48766676365204,266905699036900,1458941915879910,7965552023094600,43444688665988700
%N A386941 a(n) = Sum_{k=0..n} (2*k+1) * binomial(2*k,k) * binomial(2*n-k-1,n-k).
%F A386941 a(n) = [x^n] 1/((1-4*x)^(3/2) * (1-x)^n).
%F A386941 G.f.: (1+sqrt(1-4*x))/sqrt( 4 * (1-4*x) * (2*sqrt(1-4*x)-1)^3 ).
%F A386941 a(n) = Sum_{k=0..n} 3^(n-k) * binomial(2*n+1/2,k) * binomial(n-k+1/2,n-k) = Sum_{k=0..n} (2*k+1) * (3/4)^k * binomial(2*k,k) * binomial(2*n+1/2,n-k).
%F A386941 a(n) = Sum_{k=0..n} 4^k * (-3)^(n-k) * binomial(2*n+1/2,k) * binomial(2*n-k-1,n-k).
%o A386941 (PARI) a(n) = sum(k=0, n, (2*k+1)*binomial(2*k, k)*binomial(2*n-k-1, n-k));
%Y A386941 Cf. A100193, A384365, A386940.
%K A386941 nonn,easy
%O A386941 0,2
%A A386941 _Seiichi Manyama_, Aug 10 2025