A209665 - OEIS

%I #13 Nov 24 2016 17:56:59

%S 1,1,8,56,524,5979,85539,1460752,29112516,661843866,16890042828,

%T 477756925128,14830113520286,501073056287725,18303233207719437,

%U 718663995114727640,30181996254384621880,1349979517537576728657,64065538251202398110415,3215056386968174418054634

%N a(n) = count of monomials, degree k=0 to n, in the power sum symmetric polynomials m(mu,k) summed over all partitions mu of n.

%C Row sums of A209664.

%H Alois P. Heinz, <a href="/A209665/b209665.txt">Table of n, a(n) for n = 0..386</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Symmetric_polynomials">Symmetric Polynomials</a>

%p b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,

%p       b(n, i-1, k) +`if`(i>n, 0, k*b(n-i, i, k))))

%p     end:

%p a:= n-> add(b(n$2, k), k=0..n):

%p seq(a(n), n=0..20);  # _Alois P. Heinz_, Nov 24 2016

%t p[n_Integer, v_] := Sum[Subscript[x, j]^n, {j, v}]; p[par_?PartitionQ, v_] := Times @@ (p[#, v] & /@ par); Tr/@ Table[Tr[(p[#, k] & /@ Partitions[l]) /. Subscript[x, _] -> 1], {l, 11}, {k, l}]

%Y Cf. A209664.

%K nonn

%O 0,3

%A _Wouter Meeussen_, Mar 11 2012

%E a(0), a(12)-a(19) from _Alois P. Heinz_, Nov 24 2016