A133348 Dimensions of certain Lie algebra (see reference for precise definition).

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

Paolo Xausa, Table of n, a(n) for n = 0..10000

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

Adjacent sequences: A133345 A133346 A133347 * A133349 A133350 A133351

Keyword

nonn,easy

Author

N. J. A. Sloane, Oct 20 2007

Status

approved