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, 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
Keywords
Programs
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Mathematica
nmax = 50; CoefficientList[Series[1/(1 + ContinuedFractionK[-x^(k (k + 1) (k + 2)/6), 1, {k, 1, nmax}]), {x, 0, nmax}], x]
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