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

1,4

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.

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

Example

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 -...

Mathematica

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

Crossrefs

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

Sequence in context: A075805 A095872 A298586 * A168463 A227871 A298226

Adjacent sequences: A217358 A217359 A217360 * A217362 A217363 A217364

Keyword

sign,easy

Author

R. J. Mathar, Oct 01 2012

Status

approved