A209671 a(n) = count of monomials, of degree k=n, in the elementary symmetric polynomials e(mu,k) summed over all partitions mu of n.

1, 5, 37, 405, 5251, 84893, 1556535, 33175957, 785671039, 20841132255, 604829604655, 19236214748061, 661348833658423, 24554370466786319, 976242978063976162, 41477168810872793493, 1872694395510428040983, 89644070894632864643651, 4531712537608857605836563

Offset

1,2

Links

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

Wikipedia, Symmetric Polynomials

Formula

Main diagonal 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[(e[#, l] & /@ Partitions[l]) /. Subscript[x, _] -> 1, {l, 10}]

Crossrefs

Cf. A209664-A209673.

Sequence in context: A179923 A190628 A333285 * A173796 A352122 A292873

Adjacent sequences: A209668 A209669 A209670 * A209672 A209673 A209674

Keyword

nonn

Author

Wouter Meeussen, Mar 11 2012

Extensions

More terms from Peter J. Taylor, Mar 02 2017

Status

approved