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

0,3

Comments

Row sums of A209664.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..386

Wikipedia, Symmetric Polynomials

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}]

Crossrefs

Cf. A209664.

Sequence in context: A218125 A098914 A009107 * A208944 A209072 A133671

Adjacent sequences: A209662 A209663 A209664 * A209666 A209667 A209668

Keyword

nonn

Author

Wouter Meeussen, Mar 11 2012

Extensions

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

Status

approved