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A131764
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Dimensions of some specific free Lie algebra.
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0
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2, 3, 10, 30, 102, 335, 1170, 4080, 14560, 52377, 190650, 698870, 2581110, 9586395, 35791358, 134215680, 505290270, 1908866960, 7233629130, 27487764474, 104715392730, 399822314775, 1529755308210, 5864061663920, 22517998136832, 86607683851185, 333599972392960, 1286742745883790, 4969489243995030, 19215358392200893, 74382032555280450, 288230376084602880
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| This is the sequence of dimensions of a free Lie algebra on some specific set of generators.
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FORMULA
| (1/n)*Sum(moebius(n/d)*2^(2*d-1), d in divisors(n))
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EXAMPLE
| a(1)=2
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PROG
| (MUPAD) a(n):=proc(n) begin 1/n*_plus(moebius(n/d)*2^(2*d-1)$d in divisors(n)) end;
(PARI) a(n)=sumdiv(n, d, 1/n*moebius(n/d)*2^(d*2-1)); /* Joerg Arndt, Jul 06 2011 */
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CROSSREFS
| Cf. A022553, A000984, A000108.
Sequence in context: A084380 A121909 A153909 * A066706 A080022 A192913
Adjacent sequences: A131761 A131762 A131763 * A131765 A131766 A131767
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KEYWORD
| nonn
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AUTHOR
| F. Chapoton (fchapoton(AT)voila.fr), Oct 04 2007
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