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 A370214 #9 Feb 12 2024 08:38:51
%S A370214 1,1,1,7,33,101,319,1226,4705,17017,61901,231837,872031,3260856,
%T A370214 12220846,46062632,174030177,657910813,2490889801,9448650829,
%U A370214 35890996733,136473161741,519476028237,1979421705602,7549358718559,28816041869476,110075383797016
%N A370214 Coefficient of x^n in the expansion of ( (1+x) / (1-x^3)^2 )^n.
%F A370214 a(n) = Sum_{k=0..floor(n/3)} binomial(2*n+k-1,k) * binomial(n,n-3*k).
%F A370214 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^3)^2 ). See A369399.
%o A370214 (PARI) a(n, s=3, t=2, u=1) = sum(k=0, n\s, binomial(t*n+k-1, k)*binomial(u*n, n-s*k));
%Y A370214 Cf. A369399.
%K A370214 nonn
%O A370214 0,4
%A A370214 _Seiichi Manyama_, Feb 12 2024