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

Author

F. Chapoton, Oct 09 2006

Keywords

• nonn
• more

Comments

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

Examples

			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].
		

Crossrefs

Cf. A000081, A098091.