This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A353173 #19 May 03 2022 11:00:27 %S A353173 1,0,1,1,5,15,70,330,1820,10858,70875,497135,3727955,29658410, %T A353173 248989676,2194891440,20231692430,194286848280,1937546532820, %U A353173 20008993160460,213436182918652,2346406693816315,26531060178217182,307987244037724262,3664579007885995952 %N A353173 Dimension of space of invariants of n-th tensor power of the 26-dimensional fundamental (or "standard") irreducible representation of F_4. %C A353173 It is known that a(n) satisfies a linear recurrence relation with polynomial coefficients. The limit of a(n+1)/a(n) is 26. %H A353173 MathOverflow, <a href="https://mathoverflow.net/questions/96149/invariants-for-the-exceptional-complex-simple-lie-algebra-f-4">Invariants for the exceptional complex simple Lie algebra F4</a> %e A353173 a(1)=0 because there is no F_4-invariant linear form on the 26-dimensional representation; a(2)=1 because there is, up to scalars, precisely one invariant quadratic form. %o A353173 (LiE) p_tensor(n,[0,0,0,1],F4)|[0,0,0,0] # Returns the value of a(n). %Y A353173 The analogous sequence for the (52-dimensional) adjoint representation of F_4 is: A179685. %Y A353173 A similar sequence for G_2 (for its 7-dimensional fundamental irreducible representation) is: A059710. %Y A353173 A similar sequence for B_2 (for its standard 5-dimensional irreducible representation) is: A095922. %Y A353173 For A_n the similar sequence (omitting some 0's) is given by the (n+1)-dimensional Catalan numbers, e.g., A005789 for A_2. %K A353173 nonn %O A353173 0,5 %A A353173 _David A. Madore_, Apr 28 2022