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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
OFFSET
1,2
LINKS
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: A138751 A112303 A336854 * A089124 A210662 A229610
KEYWORD
nonn,tabl
AUTHOR
Wouter Meeussen, Mar 11 2012
STATUS
approved