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Coefficients in the expansion of 1/([r]-[2r]x+[3r]x^2-...); []=floor, r=3e/5.
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%I #6 Jul 13 2017 21:17:05

%S 1,3,5,9,17,30,52,91,160,281,494,871,1537,2711,4782,8437,14885,26258,

%T 46320,81712,144145,254277,448555,791273,1395843,2462330,4343663,

%U 7662423,13516866,23844368,42062554,74200268,130892661,230900629,407319256,718529778

%N Coefficients in the expansion of 1/([r]-[2r]x+[3r]x^2-...); []=floor, r=3e/5.

%C Conjecture: the sequence is strictly increasing.

%F G.f.: 1/(Sum_{k>=0} [(k+1)*r)](-x)^k), where r = 3e/5 and [ ] = floor.

%t r = 3E/5;

%t u = 1000; (* # initial terms from given series *)

%t v = 100; (* # coefficients in reciprocal series *)

%t CoefficientList[Series[1/Sum[Floor[r*(k + 1)] (-x)^k, {k, 0, u}], {x, 0, v}], x]

%Y Cf. A078140 (includes guide to related sequences).

%K nonn,easy

%O 0,2

%A _Clark Kimberling_, Jul 11 2017