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 A370195 #12 Apr 30 2024 15:56:06
%S A370195 1,2,10,56,322,1902,11440,69680,428418,2653292,16527910,103443144,
%T A370195 649964176,4097464490,25904239560,164168677056,1042651014018,
%U A370195 6634470805556,42286359318364,269925368946896,1725325033144622,11041442722096094,70739175615642016
%N A370195 Coefficient of x^n in the expansion of ( (1+x)^2 * (1+x^2)^2 )^n.
%F A370195 a(n) = Sum_{k=0..floor(n/2)} binomial(2*n,k) * binomial(2*n,n-2*k).
%F A370195 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^2)^2) ). See A369441.
%t A370195 a[n_]:=SeriesCoefficient[((1+x)^2*(1+x^2)^2)^n,{x,0,n}]; Array[a,23,0] (* _Stefano Spezia_, Apr 30 2024 *)
%o A370195 (PARI) a(n, s=2, t=2, u=2) = sum(k=0, n\s, binomial(t*n, k)*binomial(u*n, n-s*k));
%Y A370195 Cf. A369441, A370160.
%K A370195 nonn,easy
%O A370195 0,2
%A A370195 _Seiichi Manyama_, Feb 11 2024