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A133348
Dimensions of certain Lie algebra (see reference for precise definition).
1
1, 32, 462, 4224, 28314, 151008, 674817, 2617472, 9038458, 28316288, 81662152, 219288576, 553361016, 1322057088, 3009057018, 6558440064, 13748813155, 27825992480, 54545269350, 103848201600, 192502703250, 348178802400, 615628210275, 1065899278080, 1809869155380
OFFSET
0,2
LINKS
Anatol N. Kirillov, Notes on Schubert, Grothendieck and key polynomials, SIGMA, Symmetry Integrability Geom. Methods Appl. 12, Paper 034, 56 p. (2016).
J. M. Landsberg and L. Manivel, The sextonions and E7 1/2, Adv. Math. 201 (2006), 143-179. [Th. 7.2(ii), case a=4]
FORMULA
G.f.: (x^6+16*x^5+70*x^4+112*x^3+70*x^2+16*x+1) / (x-1)^16. - Colin Barker, Jul 27 2013
MAPLE
b:=binomial; t72b:= proc(a, k) ((a+k+1)/(a+1)) * b(k+2*a+1, k)*b(k+3*a/2+1, k)/(b(k+a/2, k)); end; [seq(t72b(4, k), k=0..28)];
MATHEMATICA
t72b[a_, k_] := (a+k+1) / (a+1) Binomial[k+2a+1, k] Binomial[k+3/2a+1, k] / Binomial[k+a/2, k];
Array[t72b[4, #]&, 30, 0] (* Paolo Xausa, Jan 10 2024 *)
CROSSREFS
Sequence in context: A283811 A066580 A076070 * A010837 A022724 A284339
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Oct 20 2007
STATUS
approved