The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A060404

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A060404

G.f.: Sum_{k >= 1} (phi(k)/k)*log(1-f(x^k)), where f(x) = (1 - sqrt(1 - 4*x)) / (2*x) - 1 is the g.f. for the Catalan numbers (A000108) C_1, C_2, C_3, ...
(history; published version)

#21 by Bruno Berselli at Mon Apr 03 10:36:06 EDT 2017

STATUS

reviewed

approved

#20 by Joerg Arndt at Mon Apr 03 09:08:03 EDT 2017

STATUS

proposed

reviewed

#19 by Alois P. Heinz at Mon Apr 03 08:54:35 EDT 2017

STATUS

editing

proposed

#18 by Alois P. Heinz at Mon Apr 03 08:53:26 EDT 2017

FORMULA

a(n) = (1/n) * Sum_{d|n} phi(n/d) * A000346(nd-1) for n>0. - Andrew Howroyd, Apr 02 2017

STATUS

proposed

editing

Discussion

Mon Apr 03

08:54

Alois P. Heinz: corrected formula: replaced n by d.

#17 by Andrew Howroyd at Sun Apr 02 15:47:57 EDT 2017

STATUS

editing

proposed

#16 by Andrew Howroyd at Sun Apr 02 15:43:21 EDT 2017

PROG

(PARI)

a(n) = sumdiv(n, d, eulerphi(n/d)*(2^(2*d-1) - binomial(2*d-1, d)))/n; \\ Andrew Howroyd, Apr 02 2017

#15 by Andrew Howroyd at Sun Apr 02 13:38:43 EDT 2017

LINKS

Andrew Howroyd, <a href="/A060404/b060404.txt">Table of n, a(n) for n = 0..200</a>

FORMULA

a(n) = (1/n) * Sum_{d|n} phi(n/d) * A000346(n-1). - Andrew Howroyd, Apr 02 2017

STATUS

approved

editing

#14 by Joerg Arndt at Mon Jan 21 07:22:40 EST 2013

STATUS

proposed

approved

#13 by Jean-Fran�ois Alcover at Mon Jan 21 07:12:40 EST 2013

STATUS

editing

proposed

#12 by Jean-Fran�ois Alcover at Mon Jan 21 07:12:33 EST 2013

MATHEMATICA

max = 25; f[x_] := (1 - Sqrt[1 - 4*x])/(2*x) - 1; gf = Sum[(EulerPhi[k]/k)*Log[1 - f[x^k]], {k, 1, max}]; CoefficientList[ Series[-gf, {x, 0, max}], x] (* Jean-Fran�ois Alcover, Jan 21 2013 *)

STATUS

approved

editing