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A025259
a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ...+ a(n-3)*a(3) for n >= 4.
1
2, -1, 1, 2, 3, 5, 11, 27, 65, 154, 371, 917, 2303, 5828, 14839, 38049, 98237, 255106, 665655, 1744318, 4588881, 12115727, 32092597, 85259160, 227117149, 606512641, 1623412007, 4354539253, 11703442343, 31512560472, 84996156243, 229621401075
OFFSET
1,1
LINKS
FORMULA
G.f.: (1+2x-x^2-sqrt(1-4x+6x^2-8x^3+x^4))/(2x)=2-x+x^2*c(x^2/(1-x)^4)/(1-x)^2, c(x) the g.f. of A000108; a(n+3)=sum{k=0..floor(n/2), C(n+3k+1,6k+1)C(k)}, where C(n)=A000108(n). - Paul Barry, May 31 2006
Conjecture: n*a(n) +2*(3-2*n)*a(n-1) +6*(n-3)*a(n-2) +4*(9-2*n)*a(n-3) +(n-6)*a(n-4)=0. - R. J. Mathar, Sep 29 2012
a(n) ~ sqrt(3*r^2-2*r^3-3*r+1) / (2 * sqrt(Pi) * n^(3/2) * r^(n+1)), where r = 2 + 1/sqrt(2/(6 + (9 + sqrt(273))^(1/3) / 3^(2/3) - 4/(3*(9 + sqrt(273)))^(1/3))) - 1/2*sqrt(24 - (2*(9 + sqrt(273))^(1/3)) / 3^(2/3) + 8/(3*(9 + sqrt(273)))^(1/3) + 44*sqrt(2/(6 + (9 + sqrt(273))^(1/3) / 3^(2/3) - 4/(3*(9 + sqrt(273)))^(1/3)))) = 0.352722901375863... is the root of the equation 1-4*r+6*r^2-8*r^3+r^4=0. - Vaclav Kotesovec, Feb 01 2014
MATHEMATICA
CoefficientList[Series[(1+2*x-x^2-Sqrt[1-4*x+6*x^2-8*x^3+x^4])/(2*x), {x, 0, 20}], x] (* Vaclav Kotesovec, Feb 01 2014 *)
CROSSREFS
Sequence in context: A288250 A169786 A191631 * A212359 A130030 A088022
KEYWORD
sign
STATUS
approved