%I #7 Dec 27 2012 23:47:15

%S 1,1,2,2,4,5,7,10,12,14,19,25,26,39,46,51,65,84,87,116,123,147,171,

%T 216,220,281,306,364,402,496,511,636,678,793,861,1032,1062,1273,1360,

%U 1569,1683,1978,2054,2428,2566,2953,3118,3627,3812,4378,4631

%N Number of partitions of n into parts <= 7 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 a211862 n = p 0 [] [1..7] 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. A026813, A098859.

%Y Cf. A105637, A211858, A211859, A211860, A211861, A211863.

%K nonn

%O 0,3

%A _Matthew C. Russell_, Apr 25 2012