OFFSET
1,3
COMMENTS
T(n,2) = A000975(n+1) because only partitions into parts of 1 and 2 contribute, so that T(n,2) = Sum_{k=0..floor(n/2)} 2^(n-2k). - Peter J. Taylor, Mar 01 2017
LINKS
Peter J. Taylor, Table of n, a(n) for n = 1..5050
Peter J. Taylor, Python program to compute terms
Wikipedia, Symmetric polynomials
FORMULA
T(n,k) = Sum_{lambda} Product_{i} binomial(k, lambda_i) where the sum is over partitions of n. - Peter J. Taylor, Mar 01 2017
EXAMPLE
Table starts as
1;
1, 5;
1, 10, 37;
1, 21, 120, 405;
1, 42, 363, 1644, 5251;
...
For n = 2, k = 2 the partitions of n are 2 and 1+1, which correspond respectively to (xy) contributing 1 and (x+y)*(x+y) contributing 4 for a total of 5. - Peter J. Taylor, Mar 01 2017
MATHEMATICA
e[n_, v_] := Tr[Times @@@ Select[Subsets[Table[Subscript[x, j], {j, v}]], Length[#] == n &]]; e[par_?PartitionQ, v_] := Times @@ (e[#, v] & /@ par); Table[Tr[(e[#, k] & /@ Partitions[l]) /. Subscript[x, _] -> 1], {l, 10}, {k, l}]
PROG
(Python) # See Taylor link
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Wouter Meeussen, Mar 11 2012
STATUS
approved