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Search: id:A072279
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| A072279 |
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Dimension of n-th graded section of a certain Lie algebra. |
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+0
9
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| 1, 4, 6, 16, 45, 144, 440, 1440, 4680, 15600, 52344, 177840, 608160, 2095920, 7262640, 25300032, 88517520, 310927680, 1095923400, 3874804560, 13737892896, 48829153920, 173949483240, 620963048160, 2220904271040, 7956987570576, 28553731537320, 102617166646800
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Dimensions of Lie algebra associated to Yang-Lee algerbra in the A. Connes and M. Dubois-Violette paper. - Roger L. Bagula (rlbagulatftn(AT)yahoo.com), May 25 2007
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LINKS
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A. Connes and M. Dubois-Violette, Yang-Mills Algebra
N. J. A. Sloane, Transforms
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FORMULA
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Product_{n=1..inf} 1/(1-x^n)^a(n) = 1/((1-x^2)*(1-4*x+x^2)).
a(n) = (1/n) * Sum_{k|n} moebius(n/k) (t1^k + t2^k), where t1, t2 are the roots of x^2-4x+1.
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MAPLE
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with (numtheory): f:= proc(n) option remember; `if`(n<1, `if`(n=0, 1, 0), 4*(f(n-1)-f(n-3)) +f(n-4)) end: c:= proc(n) option remember; local j; n*f(n) -add(c(j)*f(n-j), j=1..n-1) end: a:= proc(n) option remember; local d; `if`(n=0, 1, add (mobius (n/d)*c(d), d=divisors(n))/n) end: seq (a(n), n=0..27); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 09 2008]
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CROSSREFS
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Inverse EULER transform of A072335 (with its initial 1 omitted).
Cf. A072337.
Sequence in context: A165799 A056421 A032295 this_sequence A038236 A083009 A127416
Adjacent sequences: A072276 A072277 A072278 this_sequence A072280 A072281 A072282
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Jul 15 2002
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com), May 16 2008 at the suggestion of R. J. Mathar
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