A292855 Expansion of 1/(1 - x - 2*x^2/(1 - 3*x^3 - 4*x^4/(1 - 5*x^5 - 6*x^6/(1 - 7*x^7 - 8*x^8/(1 - ...))))), a continued fraction.

1, 1, 3, 5, 11, 27, 63, 143, 341, 799, 1865, 4417, 10401, 24433, 57619, 135749, 319683, 753427, 1775207, 4182359, 9855389, 23222687, 54718921, 128937361, 303821873, 715906625, 1686933723, 3975020013, 9366551195, 22070960907, 52007117407, 122547413479, 288765804957, 680436157615

Offset: 0

Author

Ilya Gutkovskiy, Sep 25 2017

Keywords

• nonn

Crossrefs

Cf. A088352, A088357.

Programs

Mathematica

nmax = 33; CoefficientList[Series[1/(1 - x + ContinuedFractionK[-2 k x^(2 k), 1 - (2 k + 1) x^(2 k + 1), {k, 1, nmax}]), {x, 0, nmax}], x]

Formula

a(n) ~ c * d^n, where d = 2.35636016857596143712421472862749989350673596686819... and c = 0.353844135039289092297842723019941866883167102736... - Vaclav Kotesovec, Sep 25 2017