cp's OEIS Frontend

A373244 T(n,k) = number of integer partitions of n into k parts for which the number of distinct parts is equal to the number of distinct multiplicities.

%I A373244 #19 Jun 02 2024 21:38:04
%S A373244 1,1,1,1,0,1,1,1,1,1,1,0,2,1,1,1,1,2,1,1,1,1,0,3,2,2,1,1,1,1,3,2,2,2,
%T A373244 1,1,1,0,4,2,3,1,2,1,1,1,1,4,3,2,4,2,2,1,1,1,0,5,3,4,5,4,2,2,1,1,1,1,
%U A373244 5,3,3,5,4,3,2,2,1,1,1,0,6,4,5,8,6,5,4,2,2,1,1,1,1,6,4,5,10,6,7,5,4,2,2,1,1
%N A373244 T(n,k) = number of integer partitions of n into k parts for which the number of distinct parts is equal to the number of distinct multiplicities.
%C A373244 Row sum is A098859 (Wilf partitions of n).
%C A373244 Counts the zeros in A373241 or A373242.
%D A373244 See references listed in A098859.
%H A373244 Alois P. Heinz, <a href="/A373244/b373244.txt">Rows n = 1..200, flattened</a> (first 40 rows from Olivier Gérard)
%e A373244 Array begins:
%e A373244   1,
%e A373244   1, 1,
%e A373244   1, 0, 1,
%e A373244   1, 1, 1, 1,
%e A373244   1, 0, 2, 1, 1,
%e A373244   1, 1, 2, 1, 1, 1,
%e A373244   1, 0, 3, 2, 2, 1, 1,
%e A373244   1, 1, 3, 2, 2, 2, 1, 1,
%e A373244   1, 0, 4, 2, 3, 1, 2, 1, 1
%e A373244   ...
%t A373244 Flatten[Table[
%t A373244   Plus @@@
%t A373244    Table[Count[
%t A373244      Map[Length[Union[#]] == Length[Union[Length /@ Split[#]]] &,
%t A373244       IntegerPartitions[n, {k}]], True], {k, 1, n}], {n, 1, 20}]]
%K A373244 nonn,tabl
%O A373244 1,13
%A A373244 _Olivier Gérard_, May 29 2024