cp's OEIS Frontend

A337583 Irregular triangle read by rows: T(n, k) is the number of integer multisets (partitions) that match the multiplicity multiset of exactly k partitions of n.

%I A337583 #12 Sep 06 2020 07:23:58
%S A337583 1,1,2,3,5,3,2,9,1,7,1,2,12,2,2,12,2,2,2,15,3,3,3,15,5,3,0,3,0,1,26,8,
%T A337583 2,1,2,0,1,1,23,7,2,4,1,3,0,1,0,0,1,28,9,4,5,2,2,2,0,0,1,1,33,11,3,4,
%U A337583 2,3,3,1,0,1,0,1,0,0,0,0,1,45,10,8,4,4,1,4,1,1,0,1,0,1,1,0,0,1,40,18,7,3,5
%N A337583 Irregular triangle read by rows: T(n, k) is the number of integer multisets (partitions) that match the multiplicity multiset of exactly k partitions of n.
%H A337583 Álvar Ibeas, <a href="/A337583/b337583.txt">Rows until n=66, flattened</a>
%H A337583 Álvar Ibeas, <a href="/A337583/a337583.txt">Rows until n=19</a>
%F A337583 Sum_{k >= 1} k * T(n, k) = A000041(n).
%e A337583 T(5, 1) = 3, T(5, 2) = 2: The partitions of 5 present A088887(5) = 5 different multiplicity multisets. Three of them are attained by a single partition of 5 (for instance, (3, 1) comes from (2, 1, 1, 1) only), whereas (1, 1) and (2, 1) arise from two partitions of 5 each (namely, (4, 1) and (3, 2) for the first and (3, 1, 1) and (2, 2, 1) for the second).
%e A337583 Triangle begins:
%e A337583   k:  1 2 3 4
%e A337583       -------
%e A337583 n=0:  1
%e A337583 n=1:  1
%e A337583 n=2:  2
%e A337583 n=3:  3
%e A337583 n=4:  5
%e A337583 n=5:  3 2
%e A337583 n=6:  9 1
%e A337583 n=7:  7 1 2
%e A337583 n=8: 12 2 2
%e A337583 n=9: 12 2 2 2
%Y A337583 Cf. A088887 (row sums), A337587 (row lengths).
%K A337583 nonn,tabf
%O A337583 0,3
%A A337583 _Álvar Ibeas_, Sep 02 2020