A209665 a(n) = count of monomials, degree k=0 to n, in the power sum symmetric polynomials m(mu,k) summed over all partitions mu of n.

1, 1, 8, 56, 524, 5979, 85539, 1460752, 29112516, 661843866, 16890042828, 477756925128, 14830113520286, 501073056287725, 18303233207719437, 718663995114727640, 30181996254384621880, 1349979517537576728657, 64065538251202398110415, 3215056386968174418054634

Offset: 0

Author

Wouter Meeussen, Mar 11 2012

Keywords

• nonn

Comments

Row sums of A209664.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..386
• Wikipedia, Symmetric Polynomials

Crossrefs

Cf. A209664.

Programs

Maple

b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
      b(n, i-1, k) +`if`(i>n, 0, k*b(n-i, i, k))))
    end:
a:= n-> add(b(n$2, k), k=0..n):
seq(a(n), n=0..20);  # Alois P. Heinz, Nov 24 2016

Mathematica

p[n_Integer, v_] := Sum[Subscript[x, j]^n, {j, v}]; p[par_?PartitionQ, v_] := Times @@ (p[#, v] & /@ par); Tr/@ Table[Tr[(p[#, k] & /@ Partitions[l]) /. Subscript[x, _] -> 1], {l, 11}, {k, l}]

Extensions

a(0), a(12)-a(19) from Alois P. Heinz, Nov 24 2016