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A254314 Hankel transform of a(n) is A006720(n). Hankel transform of a(n+1) is A006720(n+2). 1
1, 1, 2, 5, 14, 43, 143, 507, 1887, 7279, 28828, 116455, 477709, 1983779, 8321474, 35203777, 150014157, 643302743, 2773997104, 12020733635, 52319374842, 228616865437, 1002544803949, 4410700121313, 19462407890220, 86111960348939, 381956399941011 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

FORMULA

G.f. A(x) satisfies 0 = (2*x-1)*A(x)^2 + (x^2-6*x+3)*A(x) + (3*x-2).

G.f.: (3 - 6*x + x^2 - sqrt( (1-4*x+x^2)^2 - 4*x^3 )) / (2*(1 - 2*x)).

Conjecture: n*a(n) +2*(-5*n+6)*a(n-1) +2*(17*n-39)*a(n-2) +6*(-8*n+27)*a(n-3) +(25*n-114)*a(n-4) +2*(-n+6)*a(n-5)=0. - R. J. Mathar, Jun 07 2016

EXAMPLE

G.f. = 1 + x + 2*x^2 + 5*x^3 + 14*x^4 + 43*x^5 + 143*x^6 + 507*x^7 + ...

MATHEMATICA

CoefficientList[Series[(3-6*x+x^2 - Sqrt[(1-4*x+x^2)^2 -4*x^3])/(2*(1 - 2*x)), {x, 0, 60}], x] (* G. C. Greubel, Aug 10 2018 *)

PROG

(PARI) {a(n) = if( n<0, 0, polcoeff( (3 - 6*x + x^2 - sqrt( (1-4*x+x^2)^2 - 4*x^3 + x^2 * O(x^n))) / (2*(1 - 2*x)), n))};

(MAGMA) m:=60; R<x>:=PowerSeriesRing(Rationals(), m); Coefficients(R!((3-6*x+x^2 - Sqrt((1-4*x+x^2)^2 -4*x^3))/(2*(1 - 2*x)))); // G. C. Greubel, Aug 10 2018

CROSSREFS

Cf. A006720.

Sequence in context: A005425 A035349 A155888 * A249562 A006789 A202060

Adjacent sequences:  A254311 A254312 A254313 * A254315 A254316 A254317

KEYWORD

nonn

AUTHOR

Michael Somos, Jan 28 2015

STATUS

approved

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Last modified July 2 15:51 EDT 2020. Contains 335404 sequences. (Running on oeis4.)