A295073 Expansion of 1/(1 - x/(1 - x^5/(1 - x^14/(1 - x^30/(1 - x^55/(1 - ... - x^(k*(k+1)*(2*k+1)/6)/(1 - ...))))))), a continued fraction.
1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 8, 11, 15, 20, 26, 34, 45, 60, 80, 107, 142, 188, 249, 330, 439, 584, 776, 1030, 1366, 1813, 2408, 3199, 4249, 5642, 7490, 9944, 13204, 17534, 23285, 30920, 41056, 54514, 72384, 96116, 127631, 169478, 225042, 298819, 396783, 526869, 699608, 928981, 1233552
Offset: 0
Keywords
Programs
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Mathematica
nmax = 53; CoefficientList[Series[1/(1 + ContinuedFractionK[-x^(k (k + 1) (2 k + 1)/6), 1, {k, 1, nmax}]), {x, 0, nmax}], x]
Formula
G.f.: 1/(1 - x/(1 - x^5/(1 - x^14/(1 - x^30/(1 - x^55/(1 - ... - x^A000330(k)/(1 - ...))))))), a continued fraction.
a(n) ~ c * d^n, where d = 1.327852426419013789340602526081665378868516025761586390361772232517175463... and c = 0.366619510178622647108505347089605503045273798338613615745637268621... - Vaclav Kotesovec, Sep 18 2021