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A209666 T(n,k) = count of degree k monomials in the complete homogeneous symmetric polynomials h(mu,k) summed over all partitions mu of n. 4
1, 2, 7, 3, 18, 55, 5, 50, 216, 631, 7, 118, 729, 2780, 8001, 11, 301, 2621, 12954, 45865, 130453, 15, 684, 8535, 55196, 241870, 820554, 2323483, 22, 1621, 28689, 241634, 1307055, 5280204, 17353028, 48916087, 30, 3620, 91749, 1012196, 6783210, 32711022, 124991685, 401709720, 1129559068 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Alois P. Heinz, Rows n = 1..141, flattened

Wikipedia, Symmetric Polynomials

EXAMPLE

Table starts as:

  1;

  2,   7;

  3,  18, 55;

  5,  50, 216,  631;

  7, 118, 729, 2780, 8001;

MAPLE

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

      add(b(n-i*j, i-1, k)*binomial(i+k-1, k-1)^j, j=0..n/i)))

    end:

T:= (n, k)-> b(n$2, k):

seq(seq(T(n, k), k=1..n), n=1..10);  # Alois P. Heinz, Mar 04 2016

MATHEMATICA

h[n_, v_] := Tr@ Apply[Times, Table[Subscript[x, j], {j, v}]^# & /@ Compositions[n, v], {1}]; h[par_?PartitionQ, v_] := Times @@ (h[#, v] & /@ par); Table[Tr[(h[#, k] & /@ Partitions[l]) /. Subscript[x, _] -> 1], {l, 10}, {k, l}]

CROSSREFS

Main diagonal is A209668; row sums are A209667.

Sequence in context: A076992 A138751 A112303 * A089124 A210662 A229610

Adjacent sequences:  A209663 A209664 A209665 * A209667 A209668 A209669

KEYWORD

nonn,tabl

AUTHOR

Wouter Meeussen, Mar 11 2012

STATUS

approved

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Last modified January 21 19:57 EST 2019. Contains 319350 sequences. (Running on oeis4.)