OFFSET
0,2
REFERENCES
Arkadij L. Onishchik and Ernest B. Vinberg, Lie Groups and Algebraic Groups, Springer Verlag, 1990, see Table 5.
LINKS
T. D. Noe, Table of n, a(n) for n = 0..1000
Joseph M. Landsberg and Laurent Manivel, The sextonions and E7 1/2, Adv. Math. 201 (2006), 143-179. [Th. 7.3, case a=8]
Samuel Lewis and Pavel Shlykov, Nakajima quiver varieties in dimension four, arXiv:2510.15160 [math.AG], 2025. See p. 30.
Index entries for linear recurrences with constant coefficients, signature (17,-136,680,-2380,6188,-12376,19448,-24310,24310,-19448,12376,-6188,2380,-680,136,-17,1).
FORMULA
a(n) = (1/517440)*binomial(n+11, 3)*binomial(n+3, 3)*binomial(n+8, 5)^2.
From G. C. Greubel, Feb 09 2025: (Start)
a(n) = (1/165)*binomial(n+8,8)*binomial(n+11,8).
G.f.: (1 + 10*x + 28*x^2 + 28*x^3 + 10*x^4 + x^5)/(1-x)^17. (End)
From Amiram Eldar, Nov 05 2025: (Start)
Sum_{n>=0} 1/a(n) = 16431542149/945 - 1761760*Pi^2.
Sum_{n>=0} (-1)^n/a(n) = 18480*Pi^2 - 19150879/105. (End)
MAPLE
b:=binomial; t73:= proc(a, k) ((2*k+a)*(k+a)/(a^2)) * b(k+a-1, k)*b(k+3*a/2-1, k)/(b(k+a/2, k)); end; [seq(t73(8, k), k=0..40)];
MATHEMATICA
Table[(Binomial[n+11, 3]Binomial[n+3, 3]Binomial[n+8, 5]^2)/517440, {n, 0, 30}] (* Harvey P. Dale, May 01 2011 *)
PROG
(Magma)
A030648:= func< n | Binomial(n+8, 8)*Binomial(n+11, 8)/165 >;
[A030648(n): n in [0..30]]; // G. C. Greubel, Feb 09 2025
(SageMath)
def A030648(n): return binomial(n+8, 8)*binomial(n+11, 8)//165
print([A030648(n) for n in range(31)]) # G. C. Greubel, Feb 09 2025
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paolo Dominici (pl.dm(AT)libero.it)
EXTENSIONS
Edited by N. J. A. Sloane, Oct 20 2007
STATUS
approved