N := 3;K := 4;

conjsize := proc( plist )
  local a, j, n, p, s:
  n := add( p, p in plist ):
  s := n!:
  for j to max( plist ) do
    a := 0:
    for p in plist do 
      if p = j then a := a + 1 fi
    od:
    s := s / ( j^a * a! )
  od:
  return( s )
end:

for M to 15 do
  start := time():
  d := M * N:
  mu := [ seq( M, i=1..N ) ]:
  s := 0:
  for lambda in combinat[partition]( d ) do
    s := s + conjsize(lambda) * combinat[Chi](mu,lambda)^K
  od:
  s := s / d!:
  printf("H(3*%a) = %a \n", d, s);
od: