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 A370183 #12 Feb 11 2024 09:16:28
%S A370183 1,2,6,23,98,432,1929,8689,39442,180248,828376,3824757,17727989,
%T A370183 82438852,384429751,1797017598,8417950626,39506701508,185718513144,
%U A370183 874346516454,4121841403488,19454625634936,91924347974883,434783188981384,2058320844378109,9752580801216182
%N A370183 Coefficient of x^n in the expansion of ( (1+x) * (1+x+x^3) )^n.
%F A370183 a(n) = Sum_{k=0..floor(n/3)} binomial(n,k) * binomial(2*n-k,n-3*k).
%F A370183 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^3)) ). See A369481.
%o A370183 (PARI) a(n, s=3, t=1, u=1) = sum(k=0, n\s, binomial(t*n, k)*binomial((t+u)*n-k, n-s*k));
%Y A370183 Cf. A116411, A370184.
%Y A370183 Cf. A369481.
%K A370183 nonn
%O A370183 0,2
%A A370183 _Seiichi Manyama_, Feb 11 2024