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
Keywords
Links
- Peter J. Taylor, Table of n, a(n) for n = 1..100
- Wikipedia, Symmetric Polynomials
Programs
-
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}]
Formula
Row sums of triangle A209669.
Extensions
More terms from Peter J. Taylor, Mar 02 2017