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%I #4 Feb 10 2017 01:10:48
%S 1,1,0,3,3,5,5,7,22,24,30,32,73,75,91,198,277,309,339,560,689,1078,
%T 1126,1567,2703,3396,3676,5086,7046,8241,10896,13072,19891,22975,
%U 27922,41597,56117,62459,77183,100793,131846,161665,191446,255225,311247,408418,467460,599970,843441
%N Expansion of Product_{k>=0} (1 + (2*k + 1)*x^(2*k+1)).
%C Sum of products of terms in all partitions of n into distinct odd parts.
%H <a href="/index/Par#partN">Index entries for related partition-counting sequences</a>
%F G.f.: Product_{k>=0} (1 + (2*k + 1)*x^(2*k+1)).
%e a(10) = 30 because we have [9, 1], [7, 3], 9*1 = 9, 7*3 = 21 and 9 + 21 = 30.
%t nmax = 48; CoefficientList[Series[Product[1 + (2 k + 1) x^(2 k + 1), {k, 0, nmax}], {x, 0, nmax}], x]
%Y Cf. A000700, A022629, A067553.
%K nonn
%O 0,4
%A _Ilya Gutkovskiy_, Feb 09 2017