OFFSET
1,2
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..995
Elżbieta Liszewska, Wojciech Młotkowski, Some relatives of the Catalan sequence, arXiv:1907.10725 [math.CO], 2019.
Thomas M. Richardson, The three 'R's and Dual Riordan Arrays, arXiv:1609.01193 [math.CO], 2016.
FORMULA
G.f.: Series_Reversion(x - 2*x^2 - 3*x^3).
a(n) ~ (13*sqrt(13) + 35)^(n-1/2) / (13^(1/4) * sqrt(Pi) * n^(3/2) * 2^(3*n-1/2)). - Vaclav Kotesovec, Aug 21 2017
EXAMPLE
G.f.: A(x) = x + 2*x^2 + 11*x^3 + 70*x^4 + 503*x^5 + 3864*x^6 + ...
Related expansions.
A(x)^2 = x^2 + 4*x^3 + 26*x^4 + 184*x^5 + 1407*x^6 + 11280*x^7 + ...
A(x)^3 = x^3 + 6*x^4 + 45*x^5 + 350*x^6 + 2844*x^7 + 23814*x^8 + ...
where x = A(x) - 2*A(x)^2 - 3*A(x)^3.
The square-root of A(x)/x is the g.f. of A222050:
sqrt(A(x)/x) = 1 + x + 5*x^2 + 30*x^3 + 209*x^4 + 1573*x^5 + 12478*x^6 + ...
MATHEMATICA
Rest[CoefficientList[InverseSeries[Series[x - 2*x^2 - 3*x^3, {x, 0, 20}], x], x]] (* Vaclav Kotesovec, Aug 21 2017 *)
PROG
(PARI) {a(n)=polcoeff(serreverse(x - 2*x^2 - 3*x^3 + x^2*O(x^n)), n)}
for(n=1, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Nov 28 2014
STATUS
approved