A276310 G.f. A(x) satisfies: x = A(x)-2*A(x)^2-2*A(x)^3.

1, 2, 10, 60, 404, 2912, 21984, 171600, 1373680, 11215776, 93039648, 781936896, 6643741440, 56973685760, 492482782208, 4286561051904, 37536888622848, 330471001126400, 2923338431270400, 25970490200202240, 231607762146309120, 2072719382680535040

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

Cf. A250886, A276314, A276315, A276316.

Sequence in context: A215002 A301625 A262001 * A372578 A098616 A082042

Adjacent sequences: A276307 A276308 A276309 * A276311 A276312 A276313

Keyword

nonn,easy

Author

Tom Richardson, Aug 29 2016

Status

approved