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 A371815 #10 Apr 07 2024 17:43:32
%S A371815 1,3,20,156,1288,10963,95132,836650,7430956,66501696,598720080,
%T A371815 5416612336,49201807276,448442474938,4099103160424,37562606691526,
%U A371815 344959939645980,3174051631201636,29254814741949680,270047153053464712,2496167217049673468
%N A371815 a(n) = Sum_{k=0..floor(n/2)} (-1)^k * binomial(4*n-2*k-1,n-2*k).
%F A371815 a(n) = [x^n] 1/((1+x^2) * (1-x)^(3*n)).
%F A371815 a(n) = binomial(4*n-1, n)*hypergeom([1, (1-n)/2, -n/2], [1/2-2*n, 1-2*n], -1). - _Stefano Spezia_, Apr 07 2024
%o A371815 (PARI) a(n) = sum(k=0, n\2, (-1)^k*binomial(4*n-2*k-1, n-2*k));
%Y A371815 Cf. A225006, A262977, A371798.
%Y A371815 Cf. A147855.
%K A371815 nonn
%O A371815 0,2
%A A371815 _Seiichi Manyama_, Apr 06 2024