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A030647 Dimension of multiples of minimal representation of complex Lie algebra F4. 1
26, 324, 2652, 16302, 81081, 342056, 1264120, 4188834, 12664184, 35405968, 92512368, 227854536, 532703874, 1189056024, 2546364040, 5253305915, 10477865970, 20265831300, 38111646300, 69848806950, 125012625075 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

Cf. table 5 of Seminar on Lie Groups and Algebraic Groups of Onishchik and Vinberg [ Springer Verlag 1990 ].

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

FORMULA

1/1617000*(2*n+11)*binomial(n+10, 3)*binomial(n+3, 3)*binomial(n+7, 4)^2

G.f.: (x+1)*(x^4+9*x^3+19*x^2+9*x+1)/(x-1)^16. - Vaclav Kotesovec, Oct 21 2012

MATHEMATICA

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 *)

PROG

(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

CROSSREFS

Sequence in context: A015800 A276285 A232064 * A202292 A010942 A022621

Adjacent sequences:  A030644 A030645 A030646 * A030648 A030649 A030650

KEYWORD

nonn,easy

AUTHOR

Paolo Dominici (pl.dm(AT)libero.it)

STATUS

approved

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Last modified February 24 06:13 EST 2018. Contains 299597 sequences. (Running on oeis4.)