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 A370185 #12 Feb 11 2024 09:16:32
%S A370185 1,2,6,26,126,612,2970,14534,71838,357884,1793296,9026976,45612450,
%T A370185 231224060,1175422590,5989693176,30586693182,156483812892,
%U A370185 801908994852,4115509738188,21149522157816,108817959549416,560500440662872,2889915938877078,14913928051929426
%N A370185 Coefficient of x^n in the expansion of (1+x+x^3)^(2*n).
%F A370185 a(n) = Sum_{k=0..floor(n/3)} binomial(2*n,k) * binomial(2*n-k,n-3*k).
%F A370185 The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x / (1+x+x^3)^2 ). See A369483.
%o A370185 (PARI) a(n, s=3, t=2, u=0) = sum(k=0, n\s, binomial(t*n, k)*binomial((t+u)*n-k, n-s*k));
%Y A370185 Cf. A370186, A370187.
%Y A370185 Cf. A369483.
%K A370185 nonn
%O A370185 0,2
%A A370185 _Seiichi Manyama_, Feb 11 2024