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 A386862 #12 Aug 06 2025 08:39:46
%S A386862 1,5,42,409,4238,45414,496996,5517929,61909878,700189606,7968994124,
%T A386862 91158632250,1047156227068,12071222381456,139569181458552,
%U A386862 1617879480097129,18796461329347238,218806784598226926,2551538498649588892,29800118958422522414,348529038403155280548
%N A386862 a(n) = Sum_{k=0..n} 2^(n-k) * binomial(2*n+1,k) * binomial(2*n-k-1,n-k).
%F A386862 a(n) = [x^n] (1+x)^(2*n+1)/(1-2*x)^n.
%F A386862 a(n) = [x^n] 1/((1-x)^2 * (1-3*x)^n).
%F A386862 a(n) = Sum_{k=0..n} 3^k * (-2)^(n-k) * (n-k+1) * binomial(2*n+1,k).
%F A386862 a(n) = Sum_{k=0..n} 3^k * (n-k+1) * binomial(n+k-1,k).
%o A386862 (PARI) a(n) = sum(k=0, n, 2^(n-k)*binomial(2*n+1, k)*binomial(2*n-k-1, n-k));
%Y A386862 Cf. A383888, A386865.
%Y A386862 Cf. A116881.
%K A386862 nonn
%O A386862 0,2
%A A386862 _Seiichi Manyama_, Aug 06 2025