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%I A325194 #4 Apr 13 2019 22:16:04
%S A325194 1,0,0,0,1,0,0,0,0,0,0,0,2,0,0,0,0,0,1,0,0,0,0,0,2,1,0,0,0,0,0,0,2,0,
%T A325194 0,0,0,0,0,0,2,3,0,0,0,0,0,0,0,0,2,3,0,0,0,0,0,0,0,0,2,4,2,0,0,0,0,0,
%U A325194 0,0,0,0,2,5,1,0,0,0,0,0,0,0,0,0,2,4,7,1,0,0,0
%N A325194 Regular triangle read by rows where T(n,k) is the number of integer partitions of n with co-rank n - k, where co-rank is the greater of the length and the largest part.
%e A325194 Triangle begins:
%e A325194   1
%e A325194   0  0
%e A325194   0  1  0
%e A325194   0  0  0  0
%e A325194   0  0  2  0  0
%e A325194   0  0  0  1  0  0
%e A325194   0  0  0  2  1  0  0
%e A325194   0  0  0  0  2  0  0  0
%e A325194   0  0  0  0  2  3  0  0  0
%e A325194   0  0  0  0  0  2  3  0  0  0
%e A325194   0  0  0  0  0  2  4  2  0  0  0
%e A325194   0  0  0  0  0  0  2  5  1  0  0  0
%e A325194   0  0  0  0  0  0  2  4  7  1  0  0  0
%e A325194   0  0  0  0  0  0  0  2  6  6  0  0  0  0
%e A325194   0  0  0  0  0  0  0  2  4  9  7  0  0  0  0
%e A325194   0  0  0  0  0  0  0  0  2  6 11  5  0  0  0  0
%e A325194   0  0  0  0  0  0  0  0  2  4 10 14  5  0  0  0  0
%e A325194   0  0  0  0  0  0  0  0  0  2  6 13 15  3  0  0  0  0
%e A325194   0  0  0  0  0  0  0  0  0  2  4 10 19 17  2  0  0  0  0
%e A325194   0  0  0  0  0  0  0  0  0  0  2  6 14 22 17  1  0  0  0  0
%e A325194   0  0  0  0  0  0  0  0  0  0  2  4 10 21 29 17  1  0  0  0  0
%e A325194 Row n = 16 counts the following partitions:
%e A325194   (8)         (72)       (64)      (533)    (444)
%e A325194   (11111111)  (711)      (622)     (542)    (3333)
%e A325194               (2211111)  (631)     (551)    (4332)
%e A325194               (3111111)  (6211)    (5222)   (4422)
%e A325194                          (61111)   (5321)   (4431)
%e A325194                          (222211)  (5411)
%e A325194                          (322111)  (32222)
%e A325194                          (331111)  (33221)
%e A325194                          (421111)  (33311)
%e A325194                          (511111)  (42221)
%e A325194                                    (43211)
%e A325194                                    (44111)
%e A325194                                    (52211)
%e A325194                                    (53111)
%t A325194 Table[Length[Select[IntegerPartitions[k],Max[Length[#],Max[#]]==n-k&]],{n,0,10},{k,0,n}]
%Y A325194 Column sums are A000041. Row sums are A325193.
%Y A325194 Cf. A051924, A071724, A096771, A115720, A263297, A325178, A325192.
%K A325194 nonn,tabl
%O A325194 0,13
%A A325194 _Gus Wiseman_, Apr 13 2019

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