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A133317
Dimensions of certain Lie algebra (see reference for precise definition).
2
1, 35, 405, 2695, 12740, 47628, 149940, 413820, 1029105, 2351635, 5010005, 10061415, 19211920, 35119280, 61799760, 105163632, 173707785, 279397755, 438775645, 674334815, 1016206884, 1504211500, 2190324500, 3141625500, 4443791625, 6205210011, 8561787885
OFFSET
0,2
COMMENTS
This is the case P(5,n) of the family of sequences defined in A132458. - Ottavio D'Antona (dantona(AT)dico.unimi.it), Oct 31 2007
LINKS
J. M. Landsberg and L. Manivel, The sextonions and E7 1/2, Adv. Math. 201 (2006), 143-179. [Th. 7.2(i), case a=2]
FORMULA
Empirical g.f.: (x+1)*(x^4+24*x^3+76*x^2+24*x+1) / (x-1)^10. - Colin Barker, Jul 27 2013
MAPLE
b:=binomial; t72a:= proc(a, k) ((2*a+2*k+1)/(2*a+1)) * b(k+3*a/2-1, k)*b(k+3*a/2+1, k)*b(k+2*a, k)/(b(k+a/2-1, k)*b(k+a/2+1, k)); end; [seq(t72a(2, k), k=0..40)];
MATHEMATICA
t72a[a_, k_] := (2k+2a+1) / (2a+1) Binomial[k+3/2a-1, k] Binomial[k+3/2a+1, k] Binomial[k+2a, k] / (Binomial[k+a/2-1, k] Binomial[k+a/2+1, k]);
Array[t72a[2, #]&, 30, 0] (* Paolo Xausa, Jan 10 2024 *)
CROSSREFS
Sequence in context: A133458 A238539 A075664 * A322879 A105947 A183846
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Oct 19 2007
STATUS
approved