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%I #15 Jun 29 2020 22:13:58
%S 1,1,1,2,3,5,5,9,11,16,20,30,34,50,58,79,96,129,152,203,243,307,375,
%T 474,563,707,850,1042,1246,1532,1815,2215,2632,3173,3765,4525,5323,
%U 6375,7519,8916,10478,12414,14523,17133,20034,23488,27422,32090,37285,43511,50559
%N Number of integer partitions of n whose multiplicities span an initial interval of positive integers.
%H Chai Wah Wu, <a href="/A317081/b317081.txt">Table of n, a(n) for n = 0..160</a>
%e The a(7) = 9 integer partitions are (7), (61), (52), (511), (43), (421), (331), (322), (3211).
%t normalQ[m_]:=Union[m]==Range[Max[m]];
%t Table[Length[Select[IntegerPartitions[n],normalQ[Length/@Split[#]]&]],{n,30}]
%o (Python)
%o from sympy.utilities.iterables import partitions
%o def A317081(n):
%o if n == 0:
%o return 1
%o c = 0
%o for d in partitions(n):
%o s = set(d.values())
%o if len(s) == max(s):
%o c += 1
%o return c # _Chai Wah Wu_, Jun 22 2020
%Y Cf. A000041, A000837, A055932, A069799, A317082, A317084, A317085, A317087, A317090.
%K nonn
%O 0,4
%A _Gus Wiseman_, Jul 21 2018
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