A251598 Dimension of space of invariant tensors in 2n-th tensor power of natural representation of Sp(8).

1, 1, 3, 15, 105, 944, 10340, 133055, 1958060, 32279090, 586453658, 11589971918, 246518371679, 5594169454700, 134456679614850, 3402014360391645, 90146180439817440, 2490533922180210720, 71468389947184389600, 2123114263550335500000

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Juan B. Gil, Peter R. W. McNamara, Jordan O. Tirrell, and Michael D. Weiner, From Dyck paths to standard Young tableaux, arXiv:1708.00513 [math.CO], 2017.

Formula

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

Prog

(LiE) p_tensor(2*n, [1, 0, 0, 0], C4)|[0, 0, 0, 0]

Crossrefs

Cf. A251593, A251594, A251596.

Sequence in context: A258498 A189919 A360579 * A338725 A295871 A293997

Adjacent sequences: A251595 A251596 A251597 * A251599 A251600 A251601

Keyword

nonn

Author

Bruce Westbury, Dec 05 2014

Status

approved