login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A083413 a(n) = Sum_{d|n} d*2^(d-1) for n > 0. 7

%I

%S 0,1,5,13,37,81,209,449,1061,2317,5205,11265,24817,53249,115141,

%T 245853,525349,1114113,2361809,4980737,10490997,22020557,46148613,

%U 96468993,201352433,419430481,872468485,1811941645,3758211557,7784628225,16106378529,33285996545

%N a(n) = Sum_{d|n} d*2^(d-1) for n > 0.

%H N. J. A. Sloane and Thomas Wieder, <a href="https://arxiv.org/abs/math/0307064">The Number of Hierarchical Orderings</a>, arXiv:math/0307064 [math.CO], 2003.

%H N. J. A. Sloane and Thomas Wieder, <a href="https://doi.org/10.1007/s11083-004-9460-9">The Number of Hierarchical Orderings</a>, Order 21 (2004), 83-89.

%F Sum_{n > 0} a(n)*x^n/n = Sum_{m > 0} x^m/(m*(1-2*x^m)).

%F G.f.: Sum_{m > 0} x^m/(1-2*x^m)^2.

%F a(n) ~ n*2^(n-2). - _Vaclav Kotesovec_, Sep 09 2014

%F L.g.f.: -log(Product_{k>=1} (1 - x^k)^(2^(k-1))) = Sum_{n>=1} a(n)*x^n/n. - _Ilya Gutkovskiy_, May 20 2018

%p oo := 101: t1 := add(x^m/(m*(1-2*x^m)),m=1..oo): series(%,x,oo): t2 := seriestolist(%): A083413 := n -> t2[n+1]*n;

%t CoefficientList[Series[Sum[x^k/(1-2*x^k)^2,{k,1,30}],{x,0,30}],x] (* _Vaclav Kotesovec_, Sep 09 2014 *)

%o (PARI) a(n)=if(n<1,0,sumdiv(n,d,d*2^(d-1)))

%Y Cf. A077272.

%Y Cf. A054599.

%K nonn

%O 0,3

%A _N. J. A. Sloane_, Jun 09 2003

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 30 06:59 EDT 2020. Contains 333119 sequences. (Running on oeis4.)