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%I #18 May 30 2024 06:58:05
%S 1,1,1,1,1,1,1,1,1,2,1,1,1,1,2,2,2,1,1,1,1,2,1,1,2,1,1,2,1,1,1,1,2,1,
%T 1,2,2,2,2,2,2,2,2,1,1,1,1,2,1,1,2,1,1,2,2,2,2,1,2,2,2,1,2,2,2,1,1,1,
%U 1,2,1,1,2,1,1,2,2,2,2,1,2,2,2,2,1,2,2,2,2,2,2,2,1,2,2,1,1,1,1,2,1,1,2,1,1,2,2,2,1,1,1,2,2,2,2,2,1,2,1,2,2,2,2,2,2,1,2,2,2,3,2,2,1,2,2,2,2,1
%N T(n,k) is the number of different multiplicities in the k-th partition of n in graded reverse lexicographic ordering (A080577).
%C The regular array for partitions of n of length k is A373270.
%C Row sums are A373271.
%H Olivier Gérard, <a href="/A373269/b373269.txt">Table of n, a(n) for n = 1..215307</a>
%e Array begins:
%e 1,
%e 1,1,
%e 1,1,1,
%e 1,1,1,2,1,
%e 1,1,1,2,2,2,1,
%e 1,1,1,2,1,1,2,1,1,2,1,
%e 1,1,1,2,1,1,2,2,2,2,2,2,2,2,1
%e ...
%e T(10,34) is the first term with value 3. It corresponds to partition 3+2+2+1+1+1 of 10, which has three different multiplicities.
%t Flatten@Table[
%t Map[Length[Union[Length /@ Split[#]]] &, IntegerPartitions[n]], {n,
%t 1, 20}]
%K nonn,tabf
%O 1,10
%A _Olivier Gérard_, May 29 2024