A302285 Expansion of 1/(1 - x - x/(1 - 2*x - x/(1 - 3*x - x/(1 - 4*x - x/(1 - 5*x - x/(1 - ...)))))), a continued fraction.

1, 2, 7, 33, 185, 1170, 8121, 60846, 486753, 4125852, 36846557, 345205559, 3381126995, 34524194712, 366635359887, 4041180951473, 46149726728969, 545161967955668, 6652026230285141, 83730953689450825, 1085924693069106823, 14494802798426546660, 198918641942013097723

Offset

0,2

Links

Table of n, a(n) for n=0..22.

Veronica Bitonti, Bishal Deb, and Alan D. Sokal, Thron-type continued fractions (T-fractions) for some classes of increasing trees, arXiv:2412.10214 [math.CO], 2024. See p. 58.

Example

G.f. A(x) = 1 + 2*x + 7*x^2 + 33*x^3 + 185*x^4 + 1170*x^5 + 8121*x^6 + 60846*x^7 + 486753*x^8 + ...

Mathematica

nmax = 22; CoefficientList[Series[1/(1 - x + ContinuedFractionK[-x, 1 - (k + 1) x, {k, 1, nmax}]), {x, 0, nmax}], x]

Crossrefs

Cf. A001515, A006318, A006351, A006789, A258173, A295289.

Sequence in context: A054727 A086618 A224769 * A249636 A172387 A186760

Adjacent sequences: A302282 A302283 A302284 * A302286 A302287 A302288

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 04 2018

Status

approved