A254316 Hankel transform of a(n) is A006720(n+1). Hankel transform of a(n+1) is A006720(n+3).

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

Offset: 0

Author

Michael Somos, Jan 28 2015

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Cf. A006720.

Programs

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 *)

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))};

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