A133317 Dimensions of certain Lie algebra (see reference for precise definition).

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

Author

N. J. A. Sloane, Oct 19 2007

Keywords

• nonn

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

• 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), 143-179. [Th. 7.2(i), case a=2]

Programs

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 *)

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