A307418 Expansion of 1/(1 - x - 2*x/(1 - 3*x - 4*x/(1 - 5*x - 6*x/(1 - 7*x - 8*x/(1 - ...))))), a continued fraction.

1, 3, 23, 297, 5377, 125211, 3564311, 119923089, 4655903809, 204870639987, 10075617486167, 547693463064633, 32607543239954113, 2110160087505699339, 147482363058886213079, 11071382656533287144481, 888443133459417946162561, 75894715974405095400952803

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Formula

a(n) ~ c * d^n * n^n, where d = 2 / (exp(1) * (2*log(2) - 1)) = 1.9046586137314438905888971496696905186344... and c = 1/sqrt(2*log(2) - 1) = 1.608943581845581629220091... - Vaclav Kotesovec, Jul 01 2019, updated Mar 18 2024

Mathematica

nmax = 17; CoefficientList[Series[1/(1 - x + ContinuedFractionK[-2 k x, 1 - (2 k + 1) x, {k, 1, nmax}]), {x, 0, nmax}], x]

Crossrefs

Cf. A001147, A001813, A292855.

Sequence in context: A052842 A333957 A343849 * A365546 A380779 A231788

Adjacent sequences: A307415 A307416 A307417 * A307419 A307420 A307421

Keyword

nonn

Author

Ilya Gutkovskiy, Jun 25 2019

Status

approved