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Search: id:A083413
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| A083413 |
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a(n) = Sum_{d|n} d*2^(d-1) for n > 0. |
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+0
4
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| 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
(list; graph; listen)
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OFFSET
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0,3
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LINKS
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N. J. A. Sloane and Thomas Wieder, The Number of Hierarchical Orderings, Order 21 (2004), 83-89.
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FORMULA
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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.
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MAPLE
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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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PROGRAM
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(PARI) a(n)=if(n<1, 0, sumdiv(n, d, d*2^(d-1)))
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CROSSREFS
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Cf. A077272.
Cf. A054599.
Sequence in context: A089523 A058507 A111057 this_sequence A071100 A125734 A129924
Adjacent sequences: A083410 A083411 A083412 this_sequence A083414 A083415 A083416
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KEYWORD
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nonn
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AUTHOR
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njas, Jun 09 2003
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