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 A370626 #10 May 01 2024 09:01:04
%S A370626 1,2,10,62,402,2662,17914,122040,839154,5811758,40482530,283311470,
%T A370626 1990464450,14030571258,99179197512,702789627712,4990636603986,
%U A370626 35506061422530,253030893941362,1805893735209486,12906043894108162,92346511605008562,661494201448139850
%N A370626 Coefficient of x^n in the expansion of 1 / (1-x-x^3)^(2*n).
%F A370626 a(n) = Sum_{k=0..floor(n/3)} binomial(2*n+k-1,k) * binomial(3*n-2*k-1,n-3*k).
%F A370626 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 A368962.
%o A370626 (PARI) a(n, s=3, t=2, u=0) = sum(k=0, n\s, binomial(t*n+k-1, k)*binomial((t-u+1)*n-(s-1)*k-1, n-s*k));
%Y A370626 Cf. A368962.
%K A370626 nonn
%O A370626 0,2
%A A370626 _Seiichi Manyama_, May 01 2024