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 A370625 #9 May 01 2024 08:58:34
%S A370625 1,0,0,3,4,5,27,63,116,354,945,2123,5563,14846,36519,93083,244068,
%T A370625 622013,1590318,4131265,10658969,27440808,71127683,184324461,
%U A370625 476969939,1237420755,3213687698,8343223779,21682184311,56400917786,146742491187,381991981659
%N A370625 Coefficient of x^n in the expansion of ( (1-x) / (1-x-x^3) )^n.
%F A370625 a(n) = Sum_{k=0..floor(n/3)} binomial(n+k-1,k) * binomial(n-2*k-1,n-3*k).
%F A370625 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) / (1-x) ).
%o A370625 (PARI) a(n, s=3, t=1, u=1) = sum(k=0, n\s, binomial(t*n+k-1, k)*binomial((t-u+1)*n-(s-1)*k-1, n-s*k));
%Y A370625 Cf. A054514.
%K A370625 nonn
%O A370625 0,4
%A A370625 _Seiichi Manyama_, May 01 2024