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 A370171 #15 May 01 2024 09:01:08
%S A370171 1,4,34,319,3146,31929,330145,3458620,36585194,389893576,4179819559,
%T A370171 45025583343,486961123577,5284324727023,57508473997848,
%U A370171 627410367071169,6859805605391466,75144918246760324,824558759018846116,9061483047671168437,99716283188165243471
%N A370171 Coefficient of x^n in the expansion of ( (1+x) * (1+x+x^2)^3 )^n.
%H A370171 Seiichi Manyama, <a href="/A370171/b370171.txt">Table of n, a(n) for n = 0..951</a>
%F A370171 a(n) = Sum_{k=0..floor(n/2)} binomial(3*n,k) * binomial(4*n-k,n-2*k).
%F A370171 The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x / ((1+x) * (1+x+x^2)^3) ). See A369479.
%o A370171 (PARI) a(n, s=2, t=3, u=1) = sum(k=0, n\s, binomial(t*n, k)*binomial((t+u)*n-k, n-s*k));
%Y A370171 Cf. A370170, A370172.
%Y A370171 Cf. A369479.
%K A370171 nonn
%O A370171 0,2
%A A370171 _Seiichi Manyama_, Feb 11 2024