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 A063018 #33 Mar 24 2023 15:19:26
%S A063018 0,1,1,3,11,44,189,850,3951,18832,91542,452075,2261753,11439372,
%T A063018 58394014,300455892,1556636807,8113709916,42518000652,223868503324,
%U A063018 1183764310960,6283573101960,33470346433605,178850415320010
%N A063018 Reversion of x - x^2 - x^3 - x^4.
%C A063018 For the reversion of x - a*x^2 - b*x^3 - c*x^4 (a!=0, b!=0, c!=0) we have a(n) = Sum(k=1,n-1, (Sum(j=0..k, a^(-n+3*k-j+1) * b^(n-3*k+2*j-1) * c^(k-j) * binomial(j,n-3*k+2*j-1) * binomial(k,j) ) ) * binomial(n+k-1,n-1))/n, n>1, a(1)=1. - _Vladimir Kruchinin_, May 28 2011
%C A063018 G.f. (with offset 1) satisfies A(x) = 1 + x*A(x)^2 + x^2*A(x)^3.
%H A063018 Vincenzo Librandi, <a href="/A063018/b063018.txt">Table of n, a(n) for n = 0..105</a>
%H A063018 Vladimir Kruchinin, <a href="https://arxiv.org/abs/1211.3244">The method for obtaining expressions for coefficients of reverse generating functions</a>, arXiv:1211.3244 [math.CO], 2012.
%H A063018 Elżbieta Liszewska, Wojciech Młotkowski, <a href="https://arxiv.org/abs/1907.10725">Some relatives of the Catalan sequence</a>, arXiv:1907.10725 [math.CO], 2019.
%H A063018 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A063018 a(n) = Sum(k=1..n-1, (Sum(j=0..k, binomial(j,n-3*k+2*j-1) * binomial(k,j))) * binomial(n+k-1,n-1))/n, n>1, a(1)=1, a(0)=0. - _Vladimir Kruchinin_, May 28 2011
%F A063018 D-finite with recurrence 2552*n*(n-1)*(n-2)*a(n) -4*(n-1)*(n-2)*(2909*n-3951)*a(n-1) -2*(n-2)*(6839*n^2 -31331*n +36576)*a(n-2) +(-17563*n^3 +138510*n^2 -359633*n +308670)*a(n-3) -120*(4*n-15)*(2*n-7)*(4*n-17)*a(n-4)=0. - _R. J. Mathar_, Mar 24 2023
%t A063018 CoefficientList[InverseSeries[Series[y - y^2 - y^3 - y^4, {y, 0, 30}], x], x]
%o A063018 (Maxima)
%o A063018 a(n):=sum((sum(binomial(j,n-3*k+2*j-1)*binomial(k,j),j,0,k))*binomial(n+k-1,n-1),k,1,n-1)/n; \\ _Vladimir Kruchinin_, May 28 2011
%o A063018 (PARI) x='x+O('x^66); /* that many terms */
%o A063018 Vec(serreverse(x-x^2-x^3-x^4)) /* show terms */ /* _Joerg Arndt_, May 28 2011 */
%Y A063018 Cf. A001002 (reversion of y - y^2 - y^3).
%K A063018 nonn,easy
%O A063018 0,4
%A A063018 _Olivier Gérard_, Jul 05 2001