login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A250886 G.f. A(x) satisfies: x = A(x) * (1 + A(x)) * (1 - 2*A(x)). 5
1, 1, 4, 15, 68, 322, 1608, 8283, 43780, 235950, 1291992, 7167030, 40192488, 227488900, 1297845008, 7455558675, 43088726148, 250362137590, 1461641062200, 8569690323810, 50438119336440, 297896152159260, 1765010252344560, 10487875429825950, 62485899131628648, 373198022044163532 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..1254

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 - x^2 - 2*x^3).

G.f. A(x) satisfies: x = -3*(1+A(x)) + 5*(1+A(x))^2 - 2*(1+A(x))^3.

a(n) ~ 2^(n - 3/2) * (10 + 7*sqrt(7))^(n - 1/2) / (7^(1/4) * sqrt(Pi) * n^(3/2) * 3^(2*n - 1)). - Vaclav Kotesovec, Aug 22 2017

EXAMPLE

G.f.: A(x) = x + x^2 + 4*x^3 + 15*x^4 + 68*x^5 + 322*x^6 + 1608*x^7 + ...

Related expansions.

A(x)^2 = x^2 + 2*x^3 + 9*x^4 + 38*x^5 + 182*x^6 + 900*x^7 + 4629*x^8 + ...

A(x)^3 = x^3 + 3*x^4 + 15*x^5 + 70*x^6 + 354*x^7 + 1827*x^8 + 9691*x^9 + ...

where x = A(x) - A(x)^2 - 2*A(x)^3.

MATHEMATICA

Rest[CoefficientList[InverseSeries[Series[x - x^2 - 2*x^3, {x, 0, 20}], x], x]] (* Vaclav Kotesovec, Aug 22 2017 *)

PROG

(PARI) {a(n)=polcoeff(serreverse(x - x^2 - 2*x^3 + x^2*O(x^n)), n)}

for(n=1, 30, print1(a(n), ", "))

CROSSREFS

Sequence in context: A102129 A164310 A011967 * A055732 A125062 A039625

Adjacent sequences:  A250883 A250884 A250885 * A250887 A250888 A250889

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Nov 28 2014

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 2 19:18 EST 2021. Contains 341756 sequences. (Running on oeis4.)