A217361 Series reversion of x+x^2+2*x^3.

1, -1, 0, 5, -16, 14, 96, -495, 880, 2002, -17888, 48178, 19040, -665380, 2501312, -1983543, -23639952, 124654250, -216770400, -722621130, 5941209120, -15657865020, -12958545600, 267306817050, -972419359392, 534946077108, 11045425672512

Offset: 1

Author

R. J. Mathar, Oct 01 2012

Keywords

• sign
• easy

Examples

			If y=x+x^2+2*x^3, then x= y -y^2 +5*y^4 -16*y^5 +14*y^6 +96*y^7 -...
		

Links

• R. J. Mathar, Table of n, a(n) for n = 1..103
• Elżbieta Liszewska, Wojciech Młotkowski, Some relatives of the Catalan sequence, arXiv:1907.10725 [math.CO], 2019.

Crossrefs

Cf. A103779 (x+x^2+x^3), A006013 (x-2*x^2+x^3).

Programs

Mathematica

Rest[CoefficientList[InverseSeries[Series[x+x^2+2*x^3,{x,0,20}],x],x]] (* Vaclav Kotesovec, Sep 10 2013 *)

Formula

D-finite with recurrence 7*n*(n-1)*a(n) +16*(n-1)*(2*n-3)*a(n-1) +12*(3*n-5)*(3*n-7)*a(n-2)=0.

Lim sup n->infinity |a(n)|^(1/n) = 6*sqrt(3/7) = 3.927922... - Vaclav Kotesovec, Sep 10 2013