A272428 Expansion of the continued fraction x/(1-pi(2)*x/(1-pi(3)*x/(1-pi(4)*x/(1-...)))).

0, 1, 1, 3, 13, 71, 461, 3447, 29093, 272767, 2797069, 30897015, 362691733, 4475707535, 57612706973, 769779683367, 10648337804645, 152377871778559, 2256813406989421, 34636615303780503

Offset: 0

Author

Benedict W. J. Irwin, Apr 29 2016

Keywords

• nonn

Comments

The initial similarity with A233824 may explain that method's success in representing pi(n).

Links

• G. C. Greubel, Table of n, a(n) for n = 0..250

Crossrefs

Cf. A000720, A233824.

Programs

Mathematica

CoefficientList[Series[x/(1 + ContinuedFractionK[-x*PrimePi[k], 1, {k, 2, 60}]), {x,0, 60}], x]

Formula

G.f.: x/(1-pi(2)*x/(1-pi(3)*x/(1-pi(4)*x/(1-...)))) a continued fraction.