A288135 Coefficients of 1/(Sum_{k>=0} [(k+1)*r]*(-x)^k), where r = sqrt(7/3) and [ ] = floor.

1, 3, 5, 9, 18, 36, 72, 144, 288, 576, 1152, 2304, 4608, 9216, 18432, 36864, 73728, 147456, 294911, 589818, 1179628, 2359242, 4718457, 9436860, 18873612, 37747008, 75493584, 150986304, 301970880, 603938304, 1207869696, 2415725568, 4831423488, 9662791680

Offset: 0

Author

Clark Kimberling, Jul 10 2017

Keywords

• nonn
• easy

Comments

Conjecture: the sequence is strictly increasing.

Crossrefs

Cf. A078140 (includes guide to related sequences).

Programs

Mathematica

r = Sqrt[7/3];
u = 1000; (* # initial terms from given series *)
v = 100;   (* # coefficients in reciprocal series *)
CoefficientList[Series[1/Sum[Floor[r*(k + 1)] (-x)^k, {k, 0, u}], {x, 0, v}], x]

Formula

G.f.: 1/(Sum_{k>=0} [(k+1)*r]*(-x)^k), where r = sqrt(7/3) and [ ] = floor.