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 A369213 #10 Jan 28 2024 10:12:33
%S A369213 1,4,23,152,1091,8264,65021,526236,4352942,36637576,312763225,
%T A369213 2701521420,23567184019,207343098824,1837623853627,16391011930424,
%U A369213 147029997389386,1325506554640872,12003342144724338,109136630802023808,995907341988015935
%N A369213 Expansion of (1/x) * Series_Reversion( x / ((1+x)^4+x^2) ).
%H A369213 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A369213 a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(n+1,k) * binomial(4*n-4*k+4,n-2*k).
%F A369213 D-finite with recurrence -3*(4813*n-632)*(3*n+2)*(3*n+4)*(n+1)*a(n) +2*(206141*n^4+1346849*n^3+118471*n^2-121301*n-7584)*a(n-1) +4*(1658281*n^4-3845638*n^3+4346111*n^2-2458136*n+406104)*a(n-2) +8*(n-2)*(2032705*n^3-6230304*n^2+5971619*n-935490)*a(n-3) +16*(n-2)*(n-3)*(958321*n^2-2152552*n+309963)*a(n-4) +544*(8765*n-1142)*(n-2)*(n-3)*(n-4)*a(n-5)=0. - _R. J. Mathar_, Jan 28 2024
%o A369213 (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)^4+x^2))/x)
%o A369213 (PARI) a(n) = sum(k=0, n\2, binomial(n+1, k)*binomial(4*n-4*k+4, n-2*k))/(n+1);
%Y A369213 Cf. A349331, A369126.
%Y A369213 Cf. A001006, A065065, A071356.
%K A369213 nonn
%O A369213 0,2
%A A369213 _Seiichi Manyama_, Jan 16 2024