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%I #17 Mar 02 2017 21:15:19
%S 1,5,37,405,5251,84893,1556535,33175957,785671039,20841132255,
%T 604829604655,19236214748061,661348833658423,24554370466786319,
%U 976242978063976162,41477168810872793493,1872694395510428040983,89644070894632864643651,4531712537608857605836563
%N a(n) = count of monomials, of degree k=n, in the elementary symmetric polynomials e(mu,k) summed over all partitions mu of n.
%H Peter J. Taylor, <a href="/A209671/b209671.txt">Table of n, a(n) for n = 1..100</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Symmetric_polynomials">Symmetric Polynomials</a>
%F Main diagonal of triangle A209669.
%t 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}]
%Y Cf. A209664-A209673.
%K nonn
%O 1,2
%A _Wouter Meeussen_, Mar 11 2012
%E More terms from _Peter J. Taylor_, Mar 02 2017
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