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A295072
Expansion of 1/(1 - x/(1 - x^4/(1 - x^10/(1 - x^20/(1 - x^35/(1 - ... - x^(k*(k+1)*(k+2)/6)/(1 - ...))))))), a continued fraction.
1
1, 1, 1, 1, 1, 2, 3, 4, 5, 7, 10, 14, 19, 26, 36, 51, 71, 98, 135, 188, 262, 364, 504, 699, 971, 1350, 1874, 2600, 3608, 5011, 6959, 9661, 13409, 18615, 25846, 35887, 49821, 69163, 96018, 133310, 185082, 256951, 356722, 495245, 687568, 954575, 1325251, 1839865, 2554325, 3546245, 4923342
OFFSET
0,6
FORMULA
G.f.: 1/(1 - x/(1 - x^4/(1 - x^10/(1 - x^20/(1 - x^35/(1 - ... - x^A000292(k)/(1 - ...))))))), a continued fraction.
a(n) ~ c * d^n, where d = 1.388323040709674097023351236945145477752521994116275726548400298175286... and c = 0.369600335108282885310522776855743258910315692223280044555536918225... - Vaclav Kotesovec, Sep 18 2021
MATHEMATICA
nmax = 50; CoefficientList[Series[1/(1 + ContinuedFractionK[-x^(k (k + 1) (k + 2)/6), 1, {k, 1, nmax}]), {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 13 2017
STATUS
approved