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A030647
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Dimension of multiples of minimal representation of complex Lie algebra F4.
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1
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26, 324, 2652, 16302, 81081, 342056, 1264120, 4188834, 12664184, 35405968, 92512368, 227854536, 532703874, 1189056024, 2546364040, 5253305915, 10477865970, 20265831300, 38111646300, 69848806950, 125012625075
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OFFSET
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1,1
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REFERENCES
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Cf. table 5 of Seminar on Lie Groups and Algebraic Groups of Onishchik and Vinberg [ Springer Verlag 1990 ].
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LINKS
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FORMULA
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1/1617000*(2*n+11)*binomial(n+10, 3)*binomial(n+3, 3)*binomial(n+7, 4)^2
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MATHEMATICA
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Rest[CoefficientList[Series[(x+1)*(x^4+9*x^3+19*x^2+9*x+1)/(x-1)^16, {x, 0, 20}], x]] (* Vaclav Kotesovec, Oct 21 2012 *)
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PROG
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(PARI) x='x+O('x^66); Vec(-1 + (x+1)*(x^4+9*x^3+19*x^2+9*x+1)/(x-1)^16) \\ Joerg Arndt, May 04 2013
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CROSSREFS
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KEYWORD
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nonn,easy
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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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