A276315 - OEIS

%I #24 Oct 15 2019 12:22:40

%S 1,3,20,165,1524,15078,156264,1674585,18404980,206325834,2350049208,

%T 27118926354,316381296840,3725407768140,44217602683728,

%U 528470024711841,6354463541900148,76818345766932450,933089010748085400,11382500895815005110,139387948563917844120

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

%H Michael De Vlieger, <a href="/A276315/b276315.txt">Table of n, a(n) for n = 1..897</a>

%H Elżbieta Liszewska, Wojciech Młotkowski, <a href="https://arxiv.org/abs/1907.10725">Some relatives of the Catalan sequence</a>, arXiv:1907.10725 [math.CO], 2019.

%H Thomas M. Richardson, <a href="http://arxiv.org/abs/1609.01193">The three 'R's and the Riordan dual</a>, arXiv:1609.01193 [math.CO], 2016.

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

%F 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

%e G.f.: A(x) = x+3*x^2+20*x^3+165*x^4+1524*x^5+15078*x^6+156264*x^7+...

%e Related Expansions:

%e A(x)^2 = x^2+6*x^3+49*x^4+450*x^5+4438*x^6+45900*x^7+491181*x^8+...

%e A(x)^3 = x^3+9*x^4+87*x^5+882*x^6+9282*x^7+100521*x^8+1113299*x^9+...

%t Rest[CoefficientList[InverseSeries[Series[x - 3*x^2 - 2*x^3, {x, 0, 20}], x],x]] (* _Vaclav Kotesovec_, Aug 22 2017 *)

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

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

%Y Cf. A250886, A276310, A276314, A276316.

%K nonn,easy

%O 1,2

%A _Tom Richardson_, Aug 29 2016