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 A369125 #12 Jan 25 2024 10:53:03
%S A369125 1,5,40,385,4095,46375,548300,6689550,83593250,1064463125,13762667750,
%T A369125 180189122750,2384130651875,31829162793750,428227113655000,
%U A369125 5800188020157500,79026653220693750,1082367047392625000,14893567523068062500,205796463286063912500
%N A369125 Expansion of (1/x) * Series_Reversion( x * ((1-x)^5+x^5) ).
%H A369125 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A369125 a(n) = (1/(n+1)) * Sum_{k=0..floor(n/5)} (-1)^k * binomial(n+k,k) * binomial(6*n+4,n-5*k).
%F A369125 D-finite with recurrence 2*n*(n-1)*(n-2)*(24115*n-65551)*(n+1)*a(n) -5*n*(n-1) *(n-2)*(392783*n^2 -1296338*n +636787)*a(n-1) +100*(n-1)*(n-2) *(86231*n^3 -471376*n^2 +844569*n -522390)*a(n-2) +50*(n-2)*(2114435*n^4 -14778692*n^3 +35712085*n^2 -33505588*n +8727216)*a(n-3) +50*(13474985*n^5 -137009240*n^4 +513119690*n^3 -832716700*n^2 +478740305*n +26151216)*a(n-4) -125*(5*n-21) *(6943*n-12944) *(5*n-19)*(5*n-18)*(5*n-17)*a(n-5)=0. - _R. J. Mathar_, Jan 25 2024
%p A369125 A369125 := proc(n)
%p A369125 add((-1)^k * binomial(n+k,k) * binomial(6*n+4,n-5*k),k=0..floor(n/5)) ;
%p A369125 %/(n+1) ;
%p A369125 end proc;
%p A369125 seq(A369125(n),n=0..70) ; # _R. J. Mathar_, Jan 25 2024
%o A369125 (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*((1-x)^5+x^5))/x)
%o A369125 (PARI) a(n) = sum(k=0, n\5, (-1)^k*binomial(n+k, k)*binomial(6*n+4, n-5*k))/(n+1);
%Y A369125 Cf. A097188, A369123, A369124.
%Y A369125 Cf. A368011.
%K A369125 nonn
%O A369125 0,2
%A A369125 _Seiichi Manyama_, Jan 13 2024