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%I #18 Jan 13 2025 11:09:55
%S 1,0,1,1,5,16,80,436,2877,21828,189877,1865175,20468437,248376198,
%T 3303397123,47785692843,746841034620,12538089887528,224955746518560,
%U 4294093811333388,86859002770470072,1855099612560598420,41698660497526383757
%N The dimension of the space of invariant tensors in the n-th tensor power of the adjoint representation of the exceptional Lie algebra E7.
%C This is known to satisfy a linear recurrence relation with polynomial coefficients. The limit of a(n+1)/a(n) is 133.
%H Bruce Westbury, <a href="/A179683/b179683.txt">Table of n, a(n) for n = 0..32</a>
%H Jacob L. Bourjaily, Michael Plesser, and Cristian Vergu, <a href="https://arxiv.org/abs/2412.21189">The Many Colours of Amplitudes</a>, arXiv:2412.21189 [hep-th], 2024. See p. 53.
%e The n-th tensor power is the trivial representation for n=0 and is the adjoint representation for n=1. For n=2 every invariant tensor is a scalar multiple of a Killing form.
%K nonn,changed
%O 0,5
%A _Bruce Westbury_, Jul 24 2010
%E More terms from _Bruce Westbury_, Nov 08 2013