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 A372371 #9 Apr 29 2024 09:29:17
%S A372371 1,1,1,7,25,61,187,666,2137,6676,22001,73217,239923,789517,2624182,
%T A372371 8729527,29026553,96790606,323546416,1082566763,3626148425,
%U A372371 12163438539,40847087821,137294721676,461890741843,1555264438186,5240857508017,17672768973979,59634361740734
%N A372371 Coefficient of x^n in the expansion of ( (1+x+x^3)^2 / (1+x) )^n.
%F A372371 a(n) = Sum_{k=0..floor(n/3)} binomial(2*n,k) * binomial(n-k,n-3*k).
%F A372371 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)^2 ). See A372375.
%o A372371 (PARI) a(n, s=3, t=2, u=-1) = sum(k=0, n\s, binomial(t*n, k)*binomial((t+u)*n-k, n-s*k));
%Y A372371 Cf. A370185, A370186, A370187.
%Y A372371 Cf. A372375.
%K A372371 nonn
%O A372371 0,4
%A A372371 _Seiichi Manyama_, Apr 28 2024