A209667 a(n) = count of monomials, of degrees k=0 to n, in the complete homogeneous symmetric polynomials h(mu,k) summed over all partitions mu of n.

1, 1, 9, 76, 902, 11635, 192205, 3450337, 73128340, 1696862300, 44414258862, 1264163699189, 39640715859359, 1340191402045395, 49097854149726795, 1924982506686743639, 80831323253459088871, 3607487926962810556542, 170964537623741430399076

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..250

Wikipedia, Symmetric Polynomials

Formula

Row sums of table A209666.

Maple

b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
      add(b(n-i*j, i-1, k)*binomial(i+k-1, k-1)^j, j=0..n/i)))
    end:
a:= n-> add(b(n$2, k), k=0..n):
seq(a(n), n=0..20);  # Alois P. Heinz, Mar 04 2016

Mathematica

h[n_, v_] := Tr@ Apply[Times, Table[Subscript[x, j], {j, v}]^# & /@ Compositions[n, v], {1}]; h[par_?PartitionQ, v_] := Times @@ (h[#, v] & /@ par); Tr/@ Table[Tr[(h[#, k] & /@ Partitions[l]) /. Subscript[x, _] -> 1], {l, 10}, {k, l}]

Crossrefs

Cf. A209664, A209665, A209666, A209667, A209668, A209669, A209670, A209671, A209672, A209673.

Sequence in context: A082677 A185818 A324354 * A276754 A075608 A330630

Adjacent sequences: A209664 A209665 A209666 * A209668 A209669 A209670

Keyword

nonn

Author

Wouter Meeussen, Mar 11 2012

Extensions

a(0), a(11)-a(18) from Alois P. Heinz, Mar 04 2016

Status

approved