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%I #26 Oct 29 2021 06:21:10
%S 1,2,3,4,9,7,6,20,26,15,10,40,72,68,30,14,75,171,220,159,56,21,133,
%T 379,614,603,352,101,29,229,786,1559,1928,1525,732,176,41,383,1568,
%U 3700,5564,5534,3618,1465,297
%N Square array T(m,n) of integer partitions with m addends n+1, read by antidiagonals.
%C T(m,n) is the integer partition with m times the addend n+1 (and no other non-one addends) given as index number of A194602.
%C The entries in the array A249544 are also in the sequence A194602. This array T contains the index numbers of A194602 corresponding to the entries of that array: A194602(T(m,n)) = A249544(m,n).
%C Row 1 is A000065, column 1 is A058695 (both with shifted index).
%H Tilman Piesk, <a href="/A249543/b249543.txt">First 113 rows of the triangle, flattened</a>
%H Tilman Piesk, <a href="https://oeis.org/A194602/a194602.txt">Table for A194602</a>
%H Li-yao Xia, <a href="/A194602/a194602_1.txt">Identities for A194602</a>
%F A194602(T(m,n)) = A249544(m,n).
%F T(1,n) = A000065(n+1) = p(n+1) - 1.
%F T(2,n) = p(2*(n+1)) - 2.
%F T(3,n) = p(3*(n+1)) - floor((n+1)/2) - 3.
%F T(m,1) = A058695(m-1) = p(2n-1).
%F p is the sequence of partition numbers A000041. (See "Identities for A194602" link.)
%e T(5,2) = 159.
%e A194602(159) = 14043. (So A249544(5,2) = 14043.)
%e 14043 in binary is 11011011011011. That corresponds to the integer partition with 5 times the addend 3. (See row 159 in "Table for A194602" link.)
%e Array begins:
%e n 1 2 3 4 5 6 7 8 9
%e m
%e 1 1 2 4 6 10 14 21 29 41
%e 2 3 9 20 40 75 133 229 383
%e 3 7 26 72 171 379 786 1568
%e 4 15 68 220 614 1559 3700
%e 5 30 159 603 1928 5564
%e 6 56 352 1525 5534
%e 7 101 732 3618
%e 8 176 1465
%e 9 297
%Y Cf. A194602, A249544, A000065, A058695, A000041.
%K nonn,tabl
%O 1,2
%A _Tilman Piesk_, Oct 31 2014
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