A209670 a(n) = count of monomials, of degrees k=1 to n, in the elementary symmetric polynomials e(mu,k) summed over all partitions mu of n.

1, 6, 48, 547, 7301, 120315, 2239803, 48278809, 1153934735, 30834749017, 900390736548, 28782727026031, 993911439932097, 37039780178206877, 1477457354215115765, 62950691931099382408, 2849385291187650049208, 136701569959985165325989, 6924379544998951633495956

Offset

1,2

Links

Peter J. Taylor, Table of n, a(n) for n = 1..100

Wikipedia, Symmetric Polynomials

Formula

Row sums of triangle A209669.

Mathematica

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

Crossrefs

Cf. A209664-A209673.

Sequence in context: A002170 A153467 A354750 * A223270 A376323 A366339

Adjacent sequences: A209667 A209668 A209669 * A209671 A209672 A209673

Keyword

nonn

Author

Wouter Meeussen, Mar 11 2012

Extensions

More terms from Peter J. Taylor, Mar 02 2017

Status

approved