A276315 G.f. A(x) satisfies: x = A(x)-3*A(x)^2-2*A(x)^3.

1, 3, 20, 165, 1524, 15078, 156264, 1674585, 18404980, 206325834, 2350049208, 27118926354, 316381296840, 3725407768140, 44217602683728, 528470024711841, 6354463541900148, 76818345766932450, 933089010748085400, 11382500895815005110, 139387948563917844120

Offset: 1

Author

Tom Richardson, Aug 29 2016

Keywords

• nonn
• easy

Examples

			G.f.: A(x) = x+3*x^2+20*x^3+165*x^4+1524*x^5+15078*x^6+156264*x^7+...
Related Expansions:
A(x)^2 = x^2+6*x^3+49*x^4+450*x^5+4438*x^6+45900*x^7+491181*x^8+...
A(x)^3 = x^3+9*x^4+87*x^5+882*x^6+9282*x^7+100521*x^8+1113299*x^9+...
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..897
• 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.

Crossrefs

Cf. A250886, A276310, A276314, A276316.

Programs

Mathematica

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

PARI

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

Formula

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

a(n) ~ (6*(18 + 5*sqrt(15))/17)^(n - 1/2) / (2*15^(1/4)*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Aug 22 2017