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A276315 G.f. A(x) satisfies: x = A(x)-3*A(x)^2-2*A(x)^3. 4
1, 3, 20, 165, 1524, 15078, 156264, 1674585, 18404980, 206325834, 2350049208, 27118926354, 316381296840, 3725407768140, 44217602683728, 528470024711841, 6354463541900148, 76818345766932450, 933089010748085400, 11382500895815005110, 139387948563917844120 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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.

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

EXAMPLE

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+...

MATHEMATICA

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

PROG

(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), ", "))

CROSSREFS

Cf. A250886, A276310, A276314, A276316.

Sequence in context: A336653 A012882 A063017 * A145329 A051643 A213377

Adjacent sequences:  A276312 A276313 A276314 * A276316 A276317 A276318

KEYWORD

nonn,easy

AUTHOR

Tom Richardson, Aug 29 2016

STATUS

approved

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Last modified February 25 19:39 EST 2021. Contains 341618 sequences. (Running on oeis4.)