A294410 Expansion of 1/(1 - x/(1 - x/(1 - 2*x^2/(1 - 2*x^2/(1 - 3*x^3/(1 - 3*x^3/(1 - ...))))))), a continued fraction.
1, 1, 2, 4, 10, 24, 64, 164, 440, 1164, 3128, 8368, 22552, 60624, 163528, 440768, 1189616, 3210000, 8667296, 23400304, 63196192, 170668608, 460972768, 1245085184, 3363190688, 9084616128, 24540062528, 66289885504, 179071151872, 483733046208, 1306740302848, 3529993576448, 9535868752256
Offset: 0
Keywords
Programs
-
Mathematica
nmax = 32; CoefficientList[Series[1/(1 + ContinuedFractionK[-Floor[(k + 1)/2] x^Floor[(k + 1)/2], 1, {k, 1, nmax}]), {x, 0, nmax}], x]
Formula
a(n) ~ c * d^n, where d = 2.7014053577058965980816004348205865476643047417470551135866... and c = 0.1473934094237780704912896884660893313026695094814554837... - Vaclav Kotesovec, Sep 16 2021