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A063022 Reversion of y - y^2 - y^3 - y^5.

%I A063022 #35 Jul 23 2023 12:46:34
%S A063022 0,1,1,3,10,39,161,698,3126,14360,67276,320229,1544257,7528577,
%T A063022 37044530,183733552,917598103,4610484729,23289784660,118209987295,
%U A063022 602556082765,3083273829240,15832177371585,81554320766310,421320423560400,2182395044437686,11332298321692704
%N A063022 Reversion of y - y^2 - y^3 - y^5.
%H A063022 Robert Israel, <a href="/A063022/b063022.txt">Table of n, a(n) for n = 0..1355</a>
%H A063022 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A063022 D-finite with recurrence 575*n*(n-1)*(n-2)*(n-3)*(20979233391541*n -77947280254859)*a(n) -(n-1)*(n-2)*(n-3)*(61583500097488301*n^2 -316279381660643613*n +324795527443572336)*a(n-1) -(n-2)*(n-3)*(38717301341634153*n^3 -324199735605145484*n^2 +891613204581594443*n -818427098922228360)*a(n-2) +5*(n-3)*(15150509582201525*n^4 -167218351234002005*n^3 +671920281600084880*n^2 -1156419009962856700*n +711178431524070144)*a(n-3) +5*(-11728771987556875*n^5 +177923469670928750*n^4 -1042517573106816125*n^3 +2912399220423080050*n^2 -3791544816675160464*n +1751906653132562208)*a(n-4) -125*(5*n-26)*(5*n-22)*(5*n-23)*(73773273715*n-209652025983)*(5*n-24)*a(n-5)=0. - _R. J. Mathar_, Mar 21 2022
%p A063022 with(gfun):
%p A063022 F:= RootOf(y-y^2-y^3-y^5-x,y):
%p A063022 DE:=holexprtodiffeq(F,g(x)):
%p A063022 Rec:= diffeqtorec(DE,g(x),a(n)):
%p A063022 f:= rectoproc(Rec,a(n),remember):
%p A063022 map(f, [$0..50]); # _Robert Israel_, Jan 08 2019
%t A063022 CoefficientList[InverseSeries[Series[y - y^2 - y^3 - y^5, {y, 0, 30}], x], x]
%o A063022 (Sage)
%o A063022 def Reversion(gf, n=30):
%o A063022     R = PowerSeriesRing(QQ, 'x', n)
%o A063022     x = R.gen().O(n)
%o A063022     return list(R(gf).reverse())
%o A063022 Reversion(x - x^2 - x^3 - x^5, 24) # _Peter Luschny_, Jan 08 2019
%Y A063022 Cf. A063019, A063023.
%K A063022 nonn,easy
%O A063022 0,4
%A A063022 _Olivier Gérard_, Jul 05 2001