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A155867 A 'Morgan Voyce' transform of the large Schroeder numbers A006318. 0
1, 3, 13, 65, 355, 2061, 12501, 78323, 503033, 3294373, 21916883, 147708777, 1006330457, 6919474163, 47956087733, 334658965641, 2349535729811, 16583609673797, 117608812053277, 837626242775875, 5988634758319665 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Image of A006318 under the Riordan array (1/(1-x), x/(1-x)^2).

LINKS

Table of n, a(n) for n=0..20.

FORMULA

G.f.: (sqrt(1 - 10x + 19x^2 - 10x^3 + x^4) - x^2 + 3x - 1)/(2x(x-1));

G.f.: 1/(1-x-2x/(1-x-x/(1-x-2x/(1-x-x/(1-x-2x/(1-x-x/(1-... (continued fraction);

a(n) = Sum_{k=0..n} C(n+k,2k)*A006318(k).

a(n) = Sum_{k=0..n} A085478(n,k)*A006318(k). - Philippe Deléham, Jan 31 2009

Conjecture: (n+1)*a(n) + (4-11*n)*a(n-1) + (29*n-43)*a(n-2) +(73-29*n)*a(n-3) + (11*n-40)*a(n-4) + (5-n)*a(n-5) = 0. - R. J. Mathar, Jul 24 2012

CROSSREFS

Sequence in context: A141342 A232222 A241598 * A009102 A080227 A199143

Adjacent sequences:  A155864 A155865 A155866 * A155868 A155869 A155870

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Jan 29 2009

STATUS

approved

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Last modified April 1 14:52 EDT 2020. Contains 333163 sequences. (Running on oeis4.)