%I #7 Dec 27 2012 23:46:53

%S 1,1,2,2,4,5,7,10,13,14,20,26,28,40,49,53,71,89,95,125,136,160,192,

%T 235,248,313,348,409,458,558,592,729,785,921,1018,1205,1264,1511,1627,

%U 1888,2037,2382,2521,2961,3143,3660,3884,4502,4782,5510

%N Number of partitions of n into parts <= 8 with the property that all parts have distinct multiplicities.

%H Doron Zeilberger, <a href="http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/dmp.html">Using generatingfunctionology to enumerate distinct-multiplicity partitions</a>.

%e For n=3 the a(3)=2 partitions are {3} and {1,1,1}. Note that {2,1} does not count, as 1 and 2 appear with the same nonzero multiplicity.

%o (Haskell)

%o a211863 n = p 0 [] [1..8] n where

%o p m ms _ 0 = if m `elem` ms then 0 else 1

%o p _ _ [] _ = 0

%o p m ms ks'@(k:ks) x

%o | x < k = 0

%o | m == 0 = p 1 ms ks' (x - k) + p 0 ms ks x

%o | m `elem` ms = p (m + 1) ms ks' (x - k)

%o | otherwise = p (m + 1) ms ks' (x - k) + p 0 (m : ms) ks x

%o -- _Reinhard Zumkeller_, Dec 27 2012

%Y Cf. A026814, A098859.

%Y Cf. A105637, A211858, A211859, A211860, A211861, A211862.

%K nonn

%O 0,3

%A _Matthew C. Russell_, Apr 25 2012