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A155862 A 'Morgan Voyce' transform of A007854. 1
1, 4, 22, 130, 790, 4870, 30274, 189202, 1186702, 7461982, 47007034, 296527162, 1872479350, 11833642006, 74833075570, 473463268642, 2996771766046, 18974162475598, 120167557286314, 761214481604554, 4822871486667526 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Hankel transform is 3^n*2^C(n+1,2).

Image of A007854 by Riordan array (1/(1-x),x/(1-x)^2).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

FORMULA

G.f.: 2/(3*sqrt(1-6x+x^2)+x-1).

G.f.: 1/(1-x-3x/(1-x-x/(1-x-x/(1-x-x/(1-x-x/(1-.... (continued fraction).

a(n) = sum{k=0..n, C(n+k,2k)*A007854(k)} = sum{k=0..n, A085478(n,k)*A007854(k)}.

Conjecture: 2*n*a(n) +(18-25*n)*a(n-1) + 41*(2*n-3)*a(n-2) +(57-25*n)*a(n-3) +2*(n-3)*a(n-4) =0. - R. J. Mathar, Nov 14 2011

a(n) ~ (1+3/sqrt(17)) * (13+3*sqrt(17))^n / 2^(2*n+2). - Vaclav Kotesovec, Feb 01 2014

MATHEMATICA

CoefficientList[Series[2/(3*Sqrt[1-6*x+x^2]+x-1), {x, 0, 20}], x] (* Vaclav Kotesovec, Feb 01 2014 *)

CROSSREFS

Cf. A001850.

Sequence in context: A199033 A086682 A261399 * A088536 A066380 A180899

Adjacent sequences:  A155859 A155860 A155861 * A155863 A155864 A155865

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Jan 29 2009

STATUS

approved

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Last modified April 6 18:51 EDT 2020. Contains 333286 sequences. (Running on oeis4.)