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A115868 Invariants for a hidden action of S_(n+1) on Cayley trees with n vertices. 0
1, 1, 1, 1, 2, 2, 4, 6, 11, 18, 39, 70, 153, 321, 721, 1612, 3792, 8896, 21498, 52230, 128994, 320786, 806582, 2040912, 5205311, 13352470, 34460430, 89384609 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,5

COMMENTS

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.

LINKS

Table of n, a(n) for n=2..29.

FORMULA

No simple formula known, only a complicated sum over partitions

EXAMPLE

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.

CROSSREFS

Cf. A000055 and A000272.

Sequence in context: A201542 A000672 A129860 * A103299 A278246 A195204

Adjacent sequences:  A115865 A115866 A115867 * A115869 A115870 A115871

KEYWORD

nonn,more

AUTHOR

F. Chapoton, Mar 14 2006

EXTENSIONS

Five more terms added by F. Chapoton, Mar 08 2020

STATUS

approved

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Last modified May 18 22:00 EDT 2022. Contains 353825 sequences. (Running on oeis4.)