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 A370160 #34 May 01 2024 09:01:16
%S A370160 1,4,32,286,2688,26004,256322,2559960,25816576,262307824,2681024032,
%T A370160 27534988936,283926200706,2937573629800,30480431060160,
%U A370160 317053438632786,3305105501423616,34519689280675808,361146528603877520,3784045825018539968,39702608870540290688
%N A370160 Coefficient of x^n in the expansion of ( (1+x)^2 * (1+x+x^2)^2 )^n.
%H A370160 Seiichi Manyama, <a href="/A370160/b370160.txt">Table of n, a(n) for n = 0..970</a>
%F A370160 a(n) = Sum_{k=0..floor(n/2)} binomial(2*n,k) * binomial(4*n-k,n-2*k).
%F A370160 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^2)^2) ). See A369478.
%t A370160 a[n_]:=SeriesCoefficient[((1+x)^2*(1+x+x^2)^2)^n,{x,0,n}]; Array[a,21,0] (* _Stefano Spezia_, Apr 30 2024 *)
%o A370160 (PARI) a(n, s=2, t=2, u=2) = sum(k=0, n\s, binomial(t*n, k)*binomial((t+u)*n-k, n-s*k));
%Y A370160 Cf. A027908, A370159.
%Y A370160 Cf. A369478, A370195.
%K A370160 nonn
%O A370160 0,2
%A A370160 _Seiichi Manyama_, Feb 11 2024