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A296201
Expansion of 1/(1 - x/(1 - x/(1 - x^2/(1 - x/(1 - x^3/(1 - x/(1 - x^4/(1 - ...)))))))), a continued fraction.
1
1, 1, 2, 4, 9, 21, 50, 120, 290, 704, 1714, 4181, 10212, 24965, 61070, 149458, 365888, 895932, 2194178, 5374262, 13164426, 32248616, 79002180, 193544446, 474168003, 1161691893, 2846131055, 6973047572, 17084140245, 41856763371, 102550935614, 251254982356, 615588531011, 1508227753087, 3695249380509
OFFSET
0,3
FORMULA
a(n) ~ c * d^n, where d = 2.450066970712861209761227155593662591019701927336233634485900133440192... and c = 0.21656595617747023258115906735909123622190252865232858964820650877171... - Vaclav Kotesovec, Sep 18 2021
MATHEMATICA
nmax = 34; CoefficientList[Series[1/(1 + ContinuedFractionK[-x^(1 + k (1 + (-1)^k)/4), 1, {k, 0, nmax}]), {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 07 2017
STATUS
approved