A250888 G.f. A(x) satisfies: x = A(x) * (1 + A(x)) * (1 - 4*A(x)).

1, 3, 22, 195, 1938, 20622, 229836, 2648547, 31301050, 377301210, 4620769140, 57333249870, 719179311732, 9105192433980, 116197502184984, 1493159297251491, 19303993468386378, 250907887026047010, 3276818401723155300, 42977976005402922330, 565863442299520006620

Offset

1,2

Links

Michael De Vlieger, Table of n, a(n) for n = 1..873

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

Formula

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

a(n) ~ 2^(n - 3/2) * 3^(n - 3/4) * (27 + 7*sqrt(21))^(n - 1/2) / (7^(1/4) * sqrt(Pi) * n^(3/2) * 5^(2*n - 1)). - Vaclav Kotesovec, Aug 22 2017

Example

G.f.: A(x) = x + 3*x^2 + 22*x^3 + 195*x^4 + 1938*x^5 + 20622*x^6 +...
Related expansions.
A(x)^2 = x^2 + 6*x^3 + 53*x^4 + 522*x^5 + 5530*x^6 + 61452*x^7 +...
A(x)^3 = x^3 + 9*x^4 + 93*x^5 + 1008*x^6 + 11370*x^7 + 132111*x^8 +...
where x = A(x) - 3*A(x)^2 - 4*A(x)^3.

Mathematica

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

Prog

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

Crossrefs

Sequence in context: A046743 A121952 A367393 * A098618 A357031 A207326

Adjacent sequences: A250885 A250886 A250887 * A250889 A250890 A250891

Keyword

nonn

Author

Paul D. Hanna, Nov 28 2014

Status

approved