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A131763 Series reversion of x(1-4x)/(1-x). 2
1, 3, 21, 183, 1785, 18651, 204141, 2310447, 26819121, 317530227, 3819724293, 46553474919, 573608632233, 7133530172619, 89423593269213, 1128765846337887, 14334721079385441, 183021615646831587 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The Hankel transform of this sequence is 12^C(n+1,2).

Number of Dyck n-paths with two colors of up (U,u) and two colors of down (D,d) avoiding UD. - David Scambler, Jun 24 2013

LINKS

Table of n, a(n) for n=0..17.

P. Barry, Embedding structures associated with Riordan arrays and moment matrices, arXiv:1312.0583 [math.CO], 2013.

FORMULA

a(n) = Sum_{k, 0<=k<=n} A086810(n,k)*3^k.

a(n) = (3/4)*A103211(n) for n>0.

a(n) = -a(n-1)+4*Sum_{i=0..n-1} a(i)*a(n-i-1)), a(0)=1. - Vladimir Kruchinin, Mar 30 2015

Conjecture: (n+1)*a(n) +7*(-2*n+1)*a(n-1) +(n-2)*a(n-2)=0. - R. J. Mathar, Aug 16 2015

MATHEMATICA

Rest[CoefficientList[InverseSeries[Series[x*(1-4*x)/(1-x), {x, 0, 20}], x], x]] (* Vaclav Kotesovec, Mar 30 2015 *)

PROG

(PARI) Vec(serreverse(x*(1-4*x)/(1-x)+ O(x^30))) \\ Michel Marcus, Mar 30 2015

CROSSREFS

Sequence in context: A192946 A216171 A054879 * A006199 A083063 A012163

Adjacent sequences:  A131760 A131761 A131762 * A131764 A131765 A131766

KEYWORD

nonn

AUTHOR

Philippe Deléham, Oct 29 2007, Nov 06 2007

EXTENSIONS

a(17) corrected by Mark van Hoeij, Jul 01 2010

STATUS

approved

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Last modified December 7 17:09 EST 2016. Contains 278888 sequences.