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 A372416 #10 Apr 30 2024 05:31:55
%S A372416 1,0,0,6,8,10,78,196,376,1446,4390,10648,32822,101426,276976,808666,
%T A372416 2449528,7046942,20491458,61124482,179376718,525065722,1556298700,
%U A372416 4598892274,13546834582,40109057710,118836735758,351539306142,1041872654824,3091535558296
%N A372416 Coefficient of x^n in the expansion of ( (1-x+x^3) / (1-x) )^(2*n).
%F A372416 a(n) = Sum_{k=0..floor(n/3)} binomial(2*n,k) * binomial(n-2*k-1,n-3*k).
%F A372416 The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x * (1-x)^2 / (1-x+x^3)^2 ). See A372418.
%o A372416 (PARI) a(n, s=3, t=2, u=2) = sum(k=0, n\s, binomial(t*n, k)*binomial((u-t+1)*n-(s-1)*k-1, n-s*k));
%Y A372416 Cf. A372417, A372418.
%K A372416 nonn
%O A372416 0,4
%A A372416 _Seiichi Manyama_, Apr 29 2024