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
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]
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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Oct 19 2007
STATUS
approved