%I A126683
%S A126683 1,1,1,2,4,8,16,33,68,144,312,686,1523,3405,7652,17284,39246,89552,
%T A126683 205253,472297,1090544,2525904,5867037,13663248,31896309,74628130,
%U A126683 174972341,411032475,967307190,2280248312,5383723722,12729879673
%N A126683 a(n) is the number of partitions of the n-th triangular number n(n+1)/
               2 into distinct odd parts.
%C A126683 Also the number of self-conjugate partitions of the n-th triangular number.
%e A126683 The 5th triangular number is 15. Writing this as a sum of distinct odd 
               numbers: 15 = 11 + 3 + 1 = 9 + 5 + 1 = 7 + 5 + 3 are all the possibilities. 
               So a(5) = 4.
%p A126683 g:=product(1+x^(2*j+1),j=0..900): seq(coeff(g,x,n*(n+1)/2),n=1..40); 
               - Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 27 2007
%Y A126683 Sequences A066655 and A104383 do the same thing for triangular numbers, 
               with partitions or distinct partitions. Sequences A072213 and A072243 
               are analogues for squares rather than triangular numbers.
%Y A126683 Sequence in context: A119610 A121485 A098588 this_sequence A005821 A004149 
               A129986
%Y A126683 Adjacent sequences: A126680 A126681 A126682 this_sequence A126684 A126685 
               A126686
%K A126683 nonn
%O A126683 1,4
%A A126683 Moshe Newman (mshnoiman(AT)hotmail.com), Feb 15 2007
%E A126683 More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 27 2007