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%I #10 Mar 08 2020 13:44:45
%S 1,1,1,1,2,2,4,6,11,18,39,70,153,321,721,1612,3792,8896,21498,52230,
%T 128994,320786,806582,2040912,5205311,13352470,34460430,89384609
%N Invariants for a hidden action of S_(n+1) on Cayley trees with n vertices.
%C This is the multiplicity of the trivial module in a sequence of modules of dimension (n-1)^(n-3) over the symmetric groups S_n. The restriction of these modules to S_(n-1) is given by the action on trees.
%F No simple formula known, only a complicated sum over partitions
%e M[6]=s[2, 1, 1, 1, 1] + 3 s[2, 2, 2] + 2 s[3, 1, 1, 1] + 2 s[3, 2, 1] + s[4, 1, 1] + 4 s[4, 2] + s[5, 1] + 2 s[6] as a sum of Schur functions hence a[6]=2.
%Y Cf. A000055 and A000272.
%K nonn,more
%O 2,5
%A _F. Chapoton_, Mar 14 2006
%E Five more terms added by _F. Chapoton_, Mar 08 2020
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