%I #5 Jul 19 2017 20:15:51
%S 1,3,5,9,18,35,66,124,234,441,829,1557,2925,5496,10325,19394,36429,
%T 68428,128532,241425,453475,851775,1599910,3005145,5644626,10602419,
%U 19914742,37406262,70260933,131972522,247886635,465610427,874565375,1642713630,3085541851
%N Coefficients of 1/(Sum_{k>=0} round((k+1)*r)(x)^k), where r = sqrt(2).
%C Conjecture: the sequence is strictly increasing.
%F G.f.: 1/(Sum_{k>=0} round((k+1)*r)(x)^k), where r = sqrt(2).
%t z = 100; r = Sqrt[2];
%t u = CoefficientList[Series[1/Sum[Round[(k + 1)*r] (x)^k, {k, 0, z}], {x, 0, z}],
%t x]; (* A289912 *)
%t v = N[u[[z]]/u[[z  1]], 200]
%t d = RealDigits[v, 10][[1]] (* A289913 *)
%Y Cf. A078140 (includes guide to related sequences), A289913.
%K nonn,easy
%O 0,2
%A _Clark Kimberling_, Jul 18 2017
