[seqfan] on a similar note...

[Wouter Meeussen]

sorry for the repeat email (Outlook crached *before* I hit the send-button!?!  and thank you, Notepad, for not craching)

the sum of all coefficients of all representations present in the decomposition of V(n-1,1)^k is cute too:
for n large it converges to :
%S A086365 1,4,15,75,428,2781,20093,159340,1372163,12725447,126238060
%N A086365 n-th Bell number of type D. A partition of {-n,...,-1,1,...,n} into nonempty subsets X_1,...,X_r is called `symmetric' if for each i -X_i = X_j for some j. a(n) is the number of such symmetric partitions such that none of the X_i are of the form {j,-j}.

I’m tempted to call this “the number of irreps into which the k’th power of the defining representation of Sn decomposes” for n large.


Wouter.

-----------------   Mathematica 4.1 implementation ---------------------
tabb = Table[(chars[{n - 1, 1}]^k cycleclasses[n]/n!).Transpose[
          chars /@ Partitions[n]], {n, 2, 14}, {k, 7}] // Transpose
Map[Tr, tabb, {2}] // MatrixForm
--------------------------------------------------------------------------