A098091 -id:A098091 - cp's OEIS frontend

A123256 Dimension of the invariant subspace in modules over the symmetric groups S_n of dimension n*(n+1)^(n-1).

1, 2, 3, 6, 10, 24, 49, 121, 289, 730, 1843, 4794, 12487

Offset: 2

F. Chapoton, Oct 09 2006

No simple formula known, just a complicated sum over partitions.

Empirically a(n+1) = sum( d divides n, A000081(d) ), this holds for the terms given. If true, this sequences starts 1, 2, 3, 6, 10, 24, 49, 121, 289, 730, 1843, 4794, 12487, 33023, 87823, 235502, 634848, 1721469, 4688677, 12826962, 35221883, 97057025, 268282856, 743729893, 2067174655, ... . - Joerg Arndt, Sep 03 2015

			a(5)=6 from the module 2 s[1, 1, 1, 1, 1] + 9 s[2, 1, 1, 1] + 14 s[2, 2, 1] + 14 s[3, 1, 1] + 14 s[3,2] + 13 s[4, 1] + 6 s[5].

Cf. A000081, A098091.

A115868 Invariants for a hidden action of S_(n+1) on Cayley trees with n vertices.

Original entry on oeis.org

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

Offset: 2

F. Chapoton, Mar 14 2006

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.

			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.

Cf. A000055 and A000272.

Cf. A000081, A051573, A098091.

No simple formula known, only a complicated sum over partitions.

It seems that a(n+1) = A000055(n) + A051573(n) - A000081(n). - Andrey Zabolotskiy, Aug 05 2024

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

cp's OEIS Frontend

A123256 Dimension of the invariant subspace in modules over the symmetric groups S_n of dimension n*(n+1)^(n-1).

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