The On-Line Encyclopedia of Integer Sequences (OEIS)

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A052861

E.g.f.: log((1-x)/(1-2*x))*x/(1-x).
(history; published version)

#18 by N. J. A. Sloane at Tue Apr 18 07:04:11 EDT 2017

LINKS

INRIA Algorithms Project, <a href="http://algoecs.inria.fr/ecsservices/ecsstructure?searchType=1&service=Search&searchTermsnbr=829">Encyclopedia of Combinatorial Structures 829</a>

Discussion

Tue Apr 18

07:04

OEIS Server: https://oeis.org/edit/global/2632

#17 by Vaclav Kotesovec at Tue Mar 17 11:06:01 EDT 2015

STATUS

editing

approved

#16 by Vaclav Kotesovec at Tue Mar 17 11:05:40 EDT 2015

FORMULA

E.g.f.: -lnlog((-1+x)/(-1+2*x))*x/(-1+x).

#15 by Vaclav Kotesovec at Tue Mar 17 11:05:19 EDT 2015

FORMULA

a(n) ~ (n-1)! * 2^n * (1 + 2/n + 6/n^2 + 26/n^3 + 150/n^4 + 1082/n^5 + 9366/n^6 + 94586/n^7), coefficients are A000629. - Vaclav Kotesovec, Oct 01 2013Mar 17 2015

CROSSREFS

Cf. A000629.

#14 by Vaclav Kotesovec at Tue Mar 17 11:02:33 EDT 2015

FORMULA

E.g.f.: -ln((-1+x)/(-1+2*x))*x/(-1+x).

Recurrence: {a(1)=0, a(0)=0, a(2)=2, (-2*n^4-12*n^3-22*n^2-12*n)*a(n)+(5*n^3+28*n^2+45*n+18)*a(n+1)+(-17*n-15-4*n^2)*a(n+2)+(n+2)*a(n+3)}.

STATUS

approved

editing

#13 by Joerg Arndt at Tue Oct 01 05:52:10 EDT 2013

STATUS

proposed

approved

#12 by Vaclav Kotesovec at Tue Oct 01 05:08:38 EDT 2013

STATUS

editing

proposed

#11 by Vaclav Kotesovec at Tue Oct 01 05:08:23 EDT 2013

FORMULA

a(n) ~ (n-1)! * 2^n. - Vaclav Kotesovec, Oct 01 2013

#10 by Vaclav Kotesovec at Tue Oct 01 05:07:44 EDT 2013

MATHEMATICA

Flatten[{0, Table[FullSimplify[-n!*(EulerGamma + I*Pi + 2^n*LerchPhi[2, 1, n] + PolyGamma[0, n])], {n, 1, 20}]}] (* Vaclav Kotesovec, Oct 01 2013 *)

#9 by Vaclav Kotesovec at Tue Oct 01 05:03:20 EDT 2013

NAME

A simple grammar.

E.g.f.: log((1-x)/(1-2*x))*x/(1-x).

COMMENTS

Previous name was: A simple grammar.

MATHEMATICA

CoefficientList[Series[Log[(1-x)/(1-2*x)]*x/(1-x), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 01 2013 *)

EXTENSIONS

New name using e.g.f., Vaclav Kotesovec, Oct 01 2013

STATUS

approved

editing