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Number of partitions of n into distinct odd composite numbers (A071904).
1

%I #6 Dec 31 2016 06:40:43

%S 1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,1,1,0,1,0,0,1,0,0,1,

%T 1,1,2,0,0,1,1,0,2,0,1,2,1,0,3,2,1,2,1,0,3,2,1,3,2,1,5,2,1,4,3,2,4,2,

%U 1,6,4,2,6,4,3,7,4,3,6,5,4,9,5,4,10,8,4,10,6,6,12,9,5,13,9,8,14,11,7,17,13,9,16,12,11,21

%N Number of partitions of n into distinct odd composite numbers (A071904).

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CompositeNumber.html">Composite Number</a>

%H <a href="/index/Par#partN">Index entries for related partition-counting sequences</a>

%F G.f.: ((1 + x^2)/(1 + x))*Product_{k>=1} (1 + x^k)/((1 + x^(2*k))*(1 + x^prime(k))).

%e a(48) = 3 because we have [39, 9], [33, 15] and [27, 21].

%t nmax = 105; CoefficientList[Series[(1 + x^2)/(1 + x) Product[(1 + x^k)/((1 + x^(2 k)) (1 + x^Prime[k])), {k, 1, nmax}], {x, 0, nmax}], x]

%Y Cf. A002095, A002808, A096258, A023895, A071904, A204389, A280285.

%K nonn

%O 0,37

%A _Ilya Gutkovskiy_, Dec 31 2016