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A038539
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Complex semisimple Lie algebras of dimension n.
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0
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1, 0, 1, 1, 0, 1, 1, 1, 2, 2, 2, 2, 2, 3, 4, 4, 4, 5, 5, 5, 8, 8, 7, 12, 12, 9, 13, 15, 15, 19, 21, 21, 23, 25, 28, 34, 35, 37, 45, 45, 45, 56, 59, 61, 77, 80, 76, 92, 100, 101, 119, 130, 133, 147, 159, 170, 188, 200, 216, 243, 251, 260, 298, 317, 329, 379, 400
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OFFSET
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1,9
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COMMENTS
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Direct consequence of classification of complex finite-dimensional simple Lie algebras
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REFERENCES
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N. Jacobson, Lie Algebras, Dover Publications.
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LINKS
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Table of n, a(n) for n=1..67.
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FORMULA
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G.f.: (1+x)/((1 - x^14)(1 - x^52)(1 - x^78)(1-x^133)(1 - x^248) prod( 1-x^(n^2 + 2n), n = 1..inf) prod(1 - x^(2n^2 + n), n=2..inf) prod(1-x^(2n^2+n), n=3..inf) prod( 1-x^(2n^2 - n), n=4..inf)).
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MATHEMATICA
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max = 67; dims = {14, 52, 78, 133, 248}; f[x_] := (1 + x)/(Times @@ (1 - x^dims)*Product[1 - x^(n^2 + 2*n), {n, 1, max}]*Product[1 - x^(2*n^2 + n), {n, 2, max}]*Product[1 - x^(2*n^2 + n), {n, 3, max}]*Product[1 - x^(2*n^2 - n), {n, 4, max}]); CoefficientList[ Series[f[x], {x, 0, max}], x] // Rest (* Jean-François Alcover, Oct 08 2012, from g.f. *)
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CROSSREFS
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Sequence in context: A199121 A109697 A103373 * A109368 A046774 A029105
Adjacent sequences: A038536 A038537 A038538 * A038540 A038541 A038542
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KEYWORD
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nonn,easy,nice
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AUTHOR
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Paolo Dominici (pl.dm(AT)libero.it)
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STATUS
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approved
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