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A254316 Hankel transform of a(n) is A006720(n+1). Hankel transform of a(n+1) is A006720(n+3). 1
1, 1, 2, 6, 21, 78, 299, 1172, 4677, 18947, 77746, 322545, 1350906, 5704822, 24265651, 103872254, 447146683, 1934538301, 8407277728, 36685185300, 160663301053, 705974374128, 3111584887543, 13752592535137, 60939737103636, 270672216346769, 1204862348053296 (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

Given g.f. A(x), 0 = (x^2-x)*A(x)^2 + (x^2-2*x+1)*A(x) + (2*x-1).

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

Conjecture: +(n+1)*a(n) +(-8*n+3)*a(n-1) +(18*n-29)*a(n-2) +(-12*n+31)*a(n-3) +(n-4)*a(n-4)=0. - R. J. Mathar, Jun 07 2016

EXAMPLE

G.f. = 1 + x + 2*x^2 + 6*x^3 + 21*x^4 + 78*x^5 + 299*x^6 + 1172*x^7 + ...

MATHEMATICA

CoefficientList[Series[(1-2*x+x^2-Sqrt[(1-4*x+x^2)^2-4*x^3])/(2*x*(1 - x)), {x, 0, 60}], x] (* G. C. Greubel, Aug 04 2018 *)

PROG

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

CROSSREFS

Cf. A006720.

Sequence in context: A129776 A129775 A235391 * A279562 A054515 A216490

Adjacent sequences:  A254313 A254314 A254315 * A254317 A254318 A254319

KEYWORD

nonn

AUTHOR

Michael Somos, Jan 28 2015

STATUS

approved

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Last modified July 8 19:01 EDT 2020. Contains 335524 sequences. (Running on oeis4.)