A083413 a(n) = Sum_{d|n} d*2^(d-1) for n > 0.
0, 1, 5, 13, 37, 81, 209, 449, 1061, 2317, 5205, 11265, 24817, 53249, 115141, 245853, 525349, 1114113, 2361809, 4980737, 10490997, 22020557, 46148613, 96468993, 201352433, 419430481, 872468485, 1811941645, 3758211557, 7784628225, 16106378529, 33285996545
Offset: 0
Keywords
Links
- N. J. A. Sloane and Thomas Wieder, The Number of Hierarchical Orderings, arXiv:math/0307064 [math.CO], 2003.
- N. J. A. Sloane and Thomas Wieder, The Number of Hierarchical Orderings, Order 21 (2004), 83-89.
Programs
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Maple
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;
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Mathematica
CoefficientList[Series[Sum[x^k/(1-2*x^k)^2,{k,1,30}],{x,0,30}],x] (* Vaclav Kotesovec, Sep 09 2014 *) -
PARI
a(n)=if(n<1,0,sumdiv(n,d,d*2^(d-1)))
Formula
Sum_{n > 0} a(n)*x^n/n = Sum_{m > 0} x^m/(m*(1-2*x^m)).
G.f.: Sum_{m > 0} x^m/(1-2*x^m)^2.
a(n) ~ n*2^(n-2). - Vaclav Kotesovec, Sep 09 2014
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