OFFSET
1,1
COMMENTS
Dimensions of certain Lie algebra (see Landsberg-Manivel reference for precise definition). - N. J. A. Sloane, Oct 15 2007
REFERENCES
Arkadij L. Onishchik and Ernest B. Vinberg, Seminar on Lie Groups and Algebraic Groups, Springer Verlag, 1990, see Table 5.
LINKS
Joseph M. Landsberg and Laurent Manivel, The sextonions and E7 1/2, Adv. Math. 201 (2006), 143-179. [Th. 7.1, case a=8]
FORMULA
a(n) = (1/298109643686752257360)*(2*n+29)*binomial(n+28, 5)*binomial(n+19, 10)* binomial(n+5, 5)*binomial(n+23, 18)^2.
Sum_{n>=1} 1/a(n) = 491726738430931097758177160178171904*log(2)/516375 - 48221792108498857154535989760*zeta(3) - 4212216716395291811283979922123713917650963/6995925956250. - Amiram Eldar, Jun 16 2026
MAPLE
b:=binomial; t71:= proc(a, k) ((3*a+2*k+5)/(3*a+5)) * b(k+2*a+3, k)*b(k+5*a/2+3, k)*b(k+3*a+4, k)/(b(k+a/2+1, k)*b(k+a+1, k)); end; [seq(t71(8, k), k=0..30)]; # N. J. A. Sloane, Oct 15 2007
MATHEMATICA
a[n_] := (1/298109643686752257360) * (2*n+29) * Binomial[n+28, 5] * Binomial[n+19, 10] * Binomial[n+5, 5] * Binomial[n+23, 18]^2; Array[a, 14] (* Amiram Eldar, Jun 16 2026 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paolo Dominici (pl.dm(AT)libero.it)
EXTENSIONS
More terms from Amiram Eldar, Jun 16 2026
STATUS
approved