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%I #8 Apr 15 2022 12:09:16
%S 1,0,0,1,0,1,0,1,2,1,2,1,4,1,4,7,6,7,6,13,8,19,8,25,34,31,34,43,60,49,
%T 84,61,134,73,158,205,232,217,280,355,378,487,450,745,572,1003,668,
%U 1381,1558,1759,1678,2383,2592,3001,3480,3865,5162,4729,6794,5953,9964
%N Number of compositions (ordered partitions) of n into distinct odd parts > 1.
%H <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%F G.f.: Sum_{k>=0} k! * x^(k*(k + 2)) / Product_{j=1..k} (1 - x^(2*j)).
%e a(12) = 4 because we have [9, 3], [7, 5], [5, 7] and [3, 9].
%t nmax = 60; CoefficientList[Series[Sum[k! x^(k (k + 2))/Product[(1 - x^(2 j)), {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]
%Y Cf. A000931, A027349, A032020, A032021, A032022, A087897.
%K nonn
%O 0,9
%A _Ilya Gutkovskiy_, Feb 03 2020