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A091561
Expansion of (1-2x-sqrt(1-4x+4x^2-4x^3))/(2x^2).
3
1, 2, 4, 9, 22, 56, 146, 388, 1048, 2869, 7942, 22192, 62510, 177308, 506008, 1451866, 4185788, 12119696, 35227748, 102753800, 300672368, 882373261, 2596389190, 7658677856, 22642421206, 67081765932, 199128719896, 592179010350
OFFSET
1,2
FORMULA
G.f.: (1-2x-sqrt(1-4x+4x^2-4x^3))/(2x^2).
a(n) = 2*a(n-1)+a(1)*a(n-3)+a(2)*a(n-4)+...+a(n-3)*a(1) for n>1.
Series reversion of g.f. A(x) is -A(-x).
G.f. A(x) satisfies 0=f(x, A(x)) where f(x, y)=(xy)^2+2(xy)-(y-x).
Conjecture: (n+2)*a(n) -2*(2*n+1)*a(n-1) +4*(n-1)*a(n-2) +2*(5-2*n)*a(n-3)=0. - R. J. Mathar, Aug 14 2012
MATHEMATICA
CoefficientList[Series[(1-2x-Sqrt[1-4x+4x^2-4x^3])/(2x^2), {x, 0, 30}], x] (* Harvey P. Dale, Jan 31 2015 *)
PROG
(PARI) a(n)=polcoeff((1-2*x-sqrt(1-4*x+4*x^2-4*x^3+x^3*O(x^n)))/2, n+2)
CROSSREFS
Sequence in context: A352702 A055588 A088456 * A025265 A152225 A037245
KEYWORD
nonn
AUTHOR
Michael Somos, Jan 20 2004
STATUS
approved