OFFSET
1,2
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..1023
Elżbieta Liszewska, Wojciech Młotkowski, Some relatives of the Catalan sequence, arXiv:1907.10725 [math.CO], 2019.
Thomas M. Richardson, The three 'R's and the Riordan dual, arXiv:1609.01193 [math.CO], 2016.
FORMULA
G.f.: Series_Reversion(x - 2*x^2 - 2*x^3).
Conjecture: 3*n*(n-1)*a(n) -13*(n-1)*(2*n-3)*a(n-1) -3*(3*n-5)*(3*n-7)*a(n-2)=0. - R. J. Mathar, Sep 17 2016
a(n) ~ (13 + 5*sqrt(10))^(n - 1/2) / (2^(5/4) * 5^(1/4) * sqrt(Pi) * n^(3/2) * 3^(n - 1/2)). - Vaclav Kotesovec, Aug 22 2017
EXAMPLE
G.f.: A(x) = x + 2*x^2 + 10*x^3 + 60*x^4 + 404*x^5 + 2912*x^6 + 21984*x^7 +...
Related expansions.
A(x)^2 = x^2 + 4*x^3 + 24*x^4 + 160*x^5 + 1148*x^6 + 8640*x^7 + 67296*x^8 +...
A(x)^3 = x^3 + 6*x^4 + 42*x^5 + 308*x^6 + 2352*x^7 + 18504*x^8 +...
where x = A(x) - 2*A(x)^2 - 2*A(x)^3.
MATHEMATICA
Rest[CoefficientList[InverseSeries[Series[x - 2*x^2 - 2*x^3, {x, 0, 20}], x], x]] (* Vaclav Kotesovec, Aug 22 2017 *)
PROG
(PARI) {a(n)=polcoeff(serreverse(x - 2*x^2 - 2*x^3 + x^2*O(x^n)), n)}
for(n=1, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Tom Richardson, Aug 29 2016
STATUS
approved