%I #24 Jan 16 2024 12:11:07
%S 1,1,3,15,105,944,10340,133055,1958060,32279090,586453658,11589971918,
%T 246518371679,5594169454700,134456679614850,3402014360391645,
%U 90146180439817440,2490533922180210720,71468389947184389600,2123114263550335500000
%N Dimension of space of invariant tensors in 2n-th tensor power of natural representation of Sp(8).
%H Juan B. Gil, Peter R. W. McNamara, Jordan O. Tirrell, and Michael D. Weiner, <a href="https://arxiv.org/abs/1708.00513">From Dyck paths to standard Young tableaux</a>, arXiv:1708.00513 [math.CO], 2017.
%F 0=256*(2*n-1)*(n-1)*(n+3)*(2*n-3)*a(n-2)-4*(2*n-1)*(10*n^3+137*n^2+521*n+432)*a(n-1)+(n+4)*(n+7)*(n+9)*(n+10)*a(n), (conjectured). - _Michael D. Weiner_, Apr 07 2016
%o (LiE) p_tensor(2*n,[1,0,0,0],C4)|[0,0,0,0]
%Y Cf. A251593, A251594, A251596.
%K nonn
%O 0,3
%A _Bruce Westbury_, Dec 05 2014