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A209665 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. 5
1, 1, 8, 56, 524, 5979, 85539, 1460752, 29112516, 661843866, 16890042828, 477756925128, 14830113520286, 501073056287725, 18303233207719437, 718663995114727640, 30181996254384621880, 1349979517537576728657, 64065538251202398110415, 3215056386968174418054634 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Row sums of A209664.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..386

Wikipedia, Symmetric Polynomials

MAPLE

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

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

    end:

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

seq(a(n), n=0..20);  # Alois P. Heinz, Nov 24 2016

MATHEMATICA

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}]

CROSSREFS

Cf. A209664.

Sequence in context: A218125 A098914 A009107 * A208944 A209072 A133671

Adjacent sequences:  A209662 A209663 A209664 * A209666 A209667 A209668

KEYWORD

nonn

AUTHOR

Wouter Meeussen, Mar 11 2012

EXTENSIONS

a(0), a(12)-a(19) from Alois P. Heinz, Nov 24 2016

STATUS

approved

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Last modified January 17 10:30 EST 2019. Contains 319218 sequences. (Running on oeis4.)