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 A370194 #15 Apr 30 2024 15:47:11
%S A370194 1,1,5,19,77,326,1391,6028,26349,116011,513730,2285570,10208111,
%T A370194 45742724,205550840,925918544,4179740909,18903381337,85635147983,
%U A370194 388517336189,1765019420602,8028115465732,36555667019338,166621503161184,760161934681647,3470945792364701
%N A370194 Coefficient of x^n in the expansion of ( (1+x) * (1+x^2)^2 )^n.
%F A370194 a(n) = Sum_{k=0..floor(n/2)} binomial(2*n,k) * binomial(n,n-2*k).
%F A370194 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^2)^2) ). See A369440.
%t A370194 a[n_]:=SeriesCoefficient[((1+x)*(1+x^2)^2)^n,{x,0,n}]; Array[a,26,0] (* _Stefano Spezia_, Apr 30 2024 *)
%o A370194 (PARI) a(n, s=2, t=2, u=1) = sum(k=0, n\s, binomial(t*n, k)*binomial(u*n, n-s*k));
%Y A370194 Cf. A369440, A370159.
%K A370194 nonn,easy
%O A370194 0,3
%A A370194 _Seiichi Manyama_, Feb 11 2024