A295836 Expansion of e.g.f. 1/(1 - x - x/((1 - x^2)^(1/2) - x/((1 - x^3)^(1/3) - x/((1 - x^4)^(1/4) - ...)))), a continued fraction.

1, 2, 10, 87, 1080, 17545, 352380, 8440425, 234965360, 7457438961, 265861218420, 10520716922485, 457671900756840, 21711259726987545, 1115540615067642764, 61720568687920627485, 3658760405598389451360, 231360521536071025523425, 15545857268826205753051620, 1106160524990742248108302221

Offset: 0

Author

Ilya Gutkovskiy, Nov 28 2017

Keywords

• nonn

Crossrefs

Cf. A088354.

Programs

Mathematica

nmax = 19; CoefficientList[Series[1/(1 - x + ContinuedFractionK[-x, (1 - x^k)^(1/k), {k, 2, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!

Formula

a(n) ~ n! * c * 4^n / n^(3/2), where c = 3.9289476103424541066892... - Vaclav Kotesovec, Nov 28 2017