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 A386617 #21 Jul 29 2025 08:40:06
%S A386617 0,1,10,81,610,4436,31626,222681,1554772,10790721,74560728,513452604,
%T A386617 3526463304,24168921568,165357919850,1129724254953,7709039995368,
%U A386617 52551835079699,357930487932282,2436038623348521,16568626556643738,112626521811112464,765201654587796312,5196570956399432796
%N A386617 a(n) = Sum_{k=0..n-1} binomial(3*k+1,k) * binomial(3*n-3*k,n-k-1).
%F A386617 G.f.: g^3 * (g-1)/(3-2*g)^2 where g=1+x*g^3.
%F A386617 G.f.: g/((1-g)^2 * (1-3*g)^2) where g*(1-g)^2 = x.
%F A386617 a(n) = Sum_{k=0..n-1} binomial(3*k+1+l,k) * binomial(3*n-3*k-l,n-k-1) for every real number l.
%F A386617 a(n) = Sum_{k=0..n-1} 2^(n-k-1) * binomial(3*n+2,k).
%F A386617 a(n) = Sum_{k=0..n-1} 3^(n-k-1) * binomial(2*n+k+2,k).
%o A386617 (PARI) a(n) = sum(k=0, n-1, binomial(3*k+1, k)*binomial(3*n-3*k, n-k-1));
%Y A386617 Cf. A006256, A036829, A062236, A075045.
%Y A386617 Cf. A006419, A386612, A386614, A386616.
%K A386617 nonn
%O A386617 0,3
%A A386617 _Seiichi Manyama_, Jul 27 2025