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

0,7

Links

Table of n, a(n) for n=0..53.

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

Mathematica

nmax = 53; CoefficientList[Series[1/(1 + ContinuedFractionK[-x^(k (k + 1) (2 k + 1)/6), 1, {k, 1, nmax}]), {x, 0, nmax}], x]

Crossrefs

Cf. A000330, A206739, A285408, A295072.

Sequence in context: A017899 A003520 A101915 * A322340 A282504 A022468

Adjacent sequences: A295070 A295071 A295072 * A295074 A295075 A295076

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 13 2017

Status

approved