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 A369126 #18 Jan 24 2024 08:25:25
%S A369126 1,4,22,140,970,7104,54096,424008,3398224,27721024,229410328,
%T A369126 1921308272,16253502512,138683973120,1192142838656,10314377770720,
%U A369126 89749921081280,784913791336192,6895599255571840,60825440855493376,538507243041624864,4783482648574893056
%N A369126 Expansion of (1/x) * Series_Reversion( x / ((1+x)^4+x^4) ).
%H A369126 Seiichi Manyama, <a href="/A369126/b369126.txt">Table of n, a(n) for n = 0..1000</a>
%H A369126 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A369126 a(n) = (1/(n+1)) * Sum_{k=0..floor(n/4)} binomial(n+1,k) * binomial(4*n-4*k+4,n-4*k).
%F A369126 D-finite with recurrence -3*(3*n+2)*(3*n+4)*(1746*n-6043)*(n+1)*a(n) +4*(519282*n^4 -1632448*n^3 +319539*n^2 +77803*n-72516)*a(n-1) +16*(-1055610*n^4 +5245655*n^3 -8423433*n^2 +5306215*n-1129842)*a(n-2) +96*(n-2) *(150552*n^3 -673240*n^2 +868987*n -301954)*a(n-3) -64*(n-2) *(n-3) *(174726*n^2 -528221*n +220460)*a(n-4) -512*(7353*n-3733)*(n-2)*(n-3)*(n-4)*a(n-5)=0. - _R. J. Mathar_, Jan 24 2024
%o A369126 (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)^4+x^4))/x)
%o A369126 (PARI) a(n) = sum(k=0, n\4, binomial(n+1, k)*binomial(4*n-4*k+4, n-4*k))/(n+1);
%Y A369126 Cf. A071356, A192132, A369128.
%Y A369126 Cf. A127902.
%K A369126 nonn
%O A369126 0,2
%A A369126 _Seiichi Manyama_, Jan 13 2024