A250885 G.f. A(x) satisfies: x = A(x) * (1 - A(x)) * (1 - 3*A(x)).

1, 4, 29, 260, 2603, 27888, 312828, 3627492, 43133255, 523068260, 6444287837, 80433798640, 1014906999988, 12924812183200, 165908765933928, 2144416925372580, 27885292408504863, 364554713774523660, 4788696579412309575, 63171942535632208740, 836566570704764498115

Offset

1,2

Links

Michael De Vlieger, Table of n, a(n) for n = 1..871

Elżbieta Liszewska, Wojciech Młotkowski, Some relatives of the Catalan sequence, arXiv:1907.10725 [math.CO], 2019.

Formula

G.f.: Series_Reversion(x - 4*x^2 + 3*x^3).

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

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

Example

G.f.: A(x) = x + 4*x^2 + 29*x^3 + 260*x^4 + 2603*x^5 + 27888*x^6 +...
Related expansions.
A(x)^2 = x^2 + 8*x^3 + 74*x^4 + 752*x^5 + 8127*x^6 + 91680*x^7 +...
A(x)^3 = x^3 + 12*x^4 + 135*x^5 + 1540*x^6 + 17964*x^7 + 213948*x^8 +...
where x = A(x) - 4*A(x)^2 + 3*A(x)^3.

Mathematica

Rest[CoefficientList[InverseSeries[Series[x - 4*x^2 + 3*x^3, {x, 0, 20}], x], x]] (* Vaclav Kotesovec, Aug 22 2017 *)

Prog

(PARI) {a(n)=polcoeff(serreverse(x - 4*x^2 + 3*x^3 + x^2*O(x^n)), n)}
for(n=1, 30, print1(a(n), ", "))

Crossrefs

Sequence in context: A367752 A254124 A203970 * A369215 A244594 A168238

Adjacent sequences: A250882 A250883 A250884 * A250886 A250887 A250888

Keyword

nonn

Author

Paul D. Hanna, Nov 28 2014

Status

approved