login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A209667 a(n) = count of monomials, of degrees k=0 to n, in the complete homogeneous symmetric polynomials h(mu,k) summed over all partitions mu of n. 4
1, 1, 9, 76, 902, 11635, 192205, 3450337, 73128340, 1696862300, 44414258862, 1264163699189, 39640715859359, 1340191402045395, 49097854149726795, 1924982506686743639, 80831323253459088871, 3607487926962810556542, 170964537623741430399076 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..250

Wikipedia, Symmetric Polynomials

FORMULA

Row sums of table A209666.

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:

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

seq(a(n), n=0..20);  # 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); Tr/@ Table[Tr[(h[#, k] & /@ Partitions[l]) /. Subscript[x, _] -> 1], {l, 10}, {k, l}]

CROSSREFS

Cf. A209664, A209665, A209666, A209667, A209668, A209669, A209670, A209671, A209672, A209673.

Sequence in context: A082677 A185818 A324354 * A276754 A075608 A282327

Adjacent sequences:  A209664 A209665 A209666 * A209668 A209669 A209670

KEYWORD

nonn

AUTHOR

Wouter Meeussen, Mar 11 2012

EXTENSIONS

a(0), a(11)-a(18) from Alois P. Heinz, Mar 04 2016

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 14 23:55 EDT 2019. Contains 328025 sequences. (Running on oeis4.)