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A071716 Expansion of (1+x^2*C)*C, where C = (1-(1-4*x)^(1/2))/(2*x) is g.f. for Catalan numbers, A000108. 4
1, 1, 3, 7, 19, 56, 174, 561, 1859, 6292, 21658, 75582, 266798, 950912, 3417340, 12369285, 45052515, 165002460, 607283490, 2244901890, 8331383610, 31030387440, 115948830660, 434542177290, 1632963760974, 6151850548776 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n) = number of lattice paths of n up steps and n down steps that start at the origin with an up step and do not cross the x-axis except possibly at (2n-2,0). - David Callan, Mar 14 2004

LINKS

Table of n, a(n) for n=0..25.

FORMULA

a(n) = A000108(n) + A000108(n-1) (Catalan numbers). - David Callan, Mar 14 2004

(n+1)*a(n) +(-3*n+1)*a(n-1) +2*(-2*n+5)*a(n-2)=0, n>=3 - R. J. Mathar, Aug 25 2013

MATHEMATICA

Join[{1, 1}, Total/@Partition[CatalanNumber[Range[30]], 2, 1]] (* Harvey P. Dale, Mar 23 2012 *)

CROSSREFS

Essentially the same as A005807.

Sequence in context: A224031 A147586 A305197 * A306088 A188625 A258171

Adjacent sequences:  A071713 A071714 A071715 * A071717 A071718 A071719

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jun 06 2002

STATUS

approved

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Last modified May 31 19:40 EDT 2020. Contains 334748 sequences. (Running on oeis4.)