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

0, 1, 1, 3, 10, 39, 161, 698, 3126, 14360, 67276, 320229, 1544257, 7528577, 37044530, 183733552, 917598103, 4610484729, 23289784660, 118209987295, 602556082765, 3083273829240, 15832177371585, 81554320766310, 421320423560400, 2182395044437686, 11332298321692704

Offset: 0

Author

Olivier Gérard, Jul 05 2001

Keywords

• nonn
• easy

Links

• Robert Israel, Table of n, a(n) for n = 0..1355
• Index entries for reversions of series

Crossrefs

Cf. A063019, A063023.

Programs

Maple

with(gfun):
F:= RootOf(y-y^2-y^3-y^5-x,y):
DE:=holexprtodiffeq(F,g(x)):
Rec:= diffeqtorec(DE,g(x),a(n)):
f:= rectoproc(Rec,a(n),remember):
map(f, [$0..50]); # Robert Israel, Jan 08 2019

Mathematica

CoefficientList[InverseSeries[Series[y - y^2 - y^3 - y^5, {y, 0, 30}], x], x]

Sage

def Reversion(gf, n=30):
    R = PowerSeriesRing(QQ, 'x', n)
    x = R.gen().O(n)
    return list(R(gf).reverse())
Reversion(x - x^2 - x^3 - x^5, 24) # Peter Luschny, Jan 08 2019

Formula

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