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

2,2

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

Links

Table of n, a(n) for n=2..14.

Example

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.

Sequence in context: A152536 A185164 A124345 * A111275 A298537 A272079

Adjacent sequences: A123253 A123254 A123255 * A123257 A123258 A123259

Keyword

nonn,more

Author

F. Chapoton, Oct 09 2006

Status

approved