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 A133351 Dimensions of certain Lie algebra (see reference for precise definition). 1
 1, 189, 6720, 103125, 945945, 6117748, 30707712, 127152180, 452615625, 1426106605, 4063625280, 10643113845, 25946898705, 59468850000, 129170145280, 267637365072, 531858496113, 1018308094245, 1885647400000, 3388127079645, 5923761615849, 10102561208916 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Paolo Xausa, Table of n, a(n) for n = 0..10000 J. M. Landsberg and L. Manivel, The sextonions and E7 1/2, Adv. Math. 201 (2006), pp. 143-179. [Th. 7.2(iii), case a = 2] FORMULA Empirical g.f.: -(x +1)*(x^8 +175*x^7 +4166*x^6 +26055*x^5 +50086*x^4 +26055*x^3 +4166*x^2 +175*x +1) / (x -1)^13. - Colin Barker, Jul 27 2013 MAPLE b:=binomial; t72c:= proc(a, k) ((4*k+3*a+2)/((3*a+2)*(k+1))) * b(k+a, k)*b(k+a+1, k)*b(k+3*a/2-1, k)*b(k+3*a/2, k)*b(2*k+2*a+1, 2*k)/ (b(k+a/2-1, k)*b(k+a/2, k)*b(2*k+a, 2*k)); end; [seq(t72c(2, k), k=0..40)]; MATHEMATICA t72c[a_, k_] := (4k+3a+2) / ((k+1)(3a+2)) Binomial[k+a, k] Binomial[k+a+1, k] Binomial[k+3/2a-1, k] Binomial[k+3/2a, k] Binomial[2k+2a+1, 2k] / (Binomial[k+a/2-1, k] Binomial[k+a/2, k] Binomial[2k+a, 2k]); Array[t72c[2, #]&, 30, 0] (* Paolo Xausa, Jan 09 2024 *) CROSSREFS Sequence in context: A297229 A211819 A266135 * A267993 A286791 A076012 Adjacent sequences: A133348 A133349 A133350 * A133352 A133353 A133354 KEYWORD nonn AUTHOR N. J. A. Sloane, Oct 20 2007 STATUS approved

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Last modified July 18 21:02 EDT 2024. Contains 374388 sequences. (Running on oeis4.)