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%I #5 Mar 30 2012 18:50:59
%S 1,0,1,1,0,1,1,0,1,2,1,1,2,1,2,3,1,2,3,1,3,4,1,2,4,2,2,5,3,3,7,4,3,6,
%T 3,5,8,4,5,8,5,5,9,6,6,12,8,6,12,8,8,13,8,8,14,10,9,16,12,10,18,13,9,
%U 19,15,14,23,16,13,22,17,14,24,20,16,29,24,16,29,24,21,33,26,21,33,29,24
%N Number of partitions of 2*n into distinct products of at least two consecutive positive integers.
%C There are no partitions of odd numbers into products of two or
%C more consecutive numbers: A137899(odd) = 0.
%H R. Zumkeller, <a href="/A137900/b137900.txt">Table of n, a(n) for n = 1..250</a>
%e a(16) = #{5*6+1*2, 2*3*4+2*3+1*2, 4*5+3*4} = 3.
%Y Cf. A045619, A137899, A000009.
%K nonn
%O 1,10
%A _Reinhard Zumkeller_, Feb 21 2008