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

0,3

Links

Table of n, a(n) for n=0..31.

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.

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

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;

Mathematica

CoefficientList[Series[Sum[x^k/(1-2*x^k)^2, {k, 1, 30}], {x, 0, 30}], x] (* Vaclav Kotesovec, Sep 09 2014 *)

Prog

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

Crossrefs

Cf. A077272.

Cf. A054599.

Sequence in context: A058507 A111057 A019268 * A232879 A269803 A298417

Adjacent sequences: A083410 A083411 A083412 * A083414 A083415 A083416

Keyword

nonn

Author

N. J. A. Sloane, Jun 09 2003

Status

approved