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%I #5 May 01 2012 14:22:51
%S 1,1,2,1,1,4,1,1,3,7,1,1,2,4,12,1,1,2,4,8,19,1,1,2,3,6,11,30,1,1,2,3,
%T 6,9,19,45,1,1,2,3,5,8,15,26,67,1,1,2,3,5,8,13,21,41,97,1,1,2,3,5,7,
%U 12,18,31,56,139,1,1,2,3,5,7,12,17,28,45,83,195,1,1,2,3,5,7,11,16,25,38,63
%N Upper right triangle of the number of m's in all partitions of n.
%C The "last" column read from the bottom is A000041.
%C Mirror of triangle A066633. - _Omar E. Pol_, May 01 2012
%e A000070: 1, 2, 4, 7, 12, 19, 30, 45, 67, 97, 139, 195, 272, 373, 508, ...,
%e A024786: 0, 1, 1, 3, 4, 8, 11, 19, 26, 41, 56, 83, 112, 160, 213, ...,
%e A024787: 0, 0, 1, 1, 2, 4, 6, 9, 15, 21, 31, 45, 63, 87, 122, ...,
%e A024788: 0, 0, 0, 1, 1, 2, 3, 6, 8, 13, 18, 28, 38, 55, 74, ...,
%e A024789: 0, 0, 0, 0, 1, 1, 2, 3, 5, 8, 12, 17, 25, 35, 50, ...,
%e A024790: 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 7, 12, 16, 24, 33, ...,
%e A024791: 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 7, 11, 16, 23, ...,
%e A024792: 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 7, 11, 15, ...,
%e A024793: 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 7, 11, ...,
%e A024794: 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 7, ...
%t (* First do ) Needs["Combinatorica`"] (* then *) f[n_, m_] := Count[Flatten@ Partitions@ n, m]; Table[ f[n, m], {n, 13}, {m, n, 1, -1}]
%Y Cf. A000041, A000070, A024786, A024787, A024788, A024789, A024790, A024791, A024792, A024793, A024794.
%K nonn,tabl
%O 1,3
%A _Robert G. Wilson v_, Aug 07 2008
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