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A217361
Series reversion of x+x^2+2*x^3.
1
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
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
KEYWORD
sign,easy
AUTHOR
R. J. Mathar, Oct 01 2012
STATUS
approved