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 A386845 #8 Aug 05 2025 10:01:56
%S A386845 1,10,143,2264,37601,642086,11165395,196658228,3496849349,62636490818,
%T A386845 1128525823927,20429545554000,371294468833193,6770529284259934,
%U A386845 123811606398566299,2269695135303598188,41697091253148057485,767476182916622450810,14149874243880085356415
%N A386845 a(n) = Sum_{k=0..n} binomial(4*n+2,k) * binomial(4*n-k,n-k).
%F A386845 a(n) = [x^n] (1+x)^(4*n+2)/(1-x)^(3*n+1).
%F A386845 a(n) = [x^n] 1/((1-x)^2 * (1-2*x)^(3*n+1)).
%F A386845 a(n) = Sum_{k=0..n} 2^k * (-1)^(n-k) * (n-k+1) * binomial(4*n+2,k).
%F A386845 a(n) = Sum_{k=0..n} 2^k * (n-k+1) * binomial(3*n+k,k).
%o A386845 (PARI) a(n) = sum(k=0, n, binomial(4*n+2, k)*binomial(4*n-k, n-k));
%Y A386845 Cf. A386843, A386844.
%K A386845 nonn
%O A386845 0,2
%A A386845 _Seiichi Manyama_, Aug 05 2025