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%I #15 May 05 2016 06:23:46
%S 1,1,1,2,2,3,4,5,6,7,9,11,13,16,19,23,27,32,38,44,52,61,71,82,95,109,
%T 126,144,165,189,215,245,278,316,358,405,458,516,581,654,734,824,923,
%U 1033,1155,1289,1438,1602,1783,1982,2202,2444,2710,3002,3323,3675,4061
%N Number of partitions of n into odd squarefree parts.
%C Also number of partitions into parts m such that 2*m is squarefree.
%H Alois P. Heinz, <a href="/A134345/b134345.txt">Table of n, a(n) for n = 0..10000</a>
%H Joerg Arndt, <a href="http://www.jjj.de/fxt/#fxtbook">Matters Computational (The Fxtbook)</a>, section 16.4.3 "Partitions into square-free parts", pp.351-352
%F G.f.: 1/prod(n>=1, 1 - moebius(2*n-1)^2 * x^(2*n-1)) = 1/prod(n>=1, 1 - moebius(2*n)^2 * x^(n)).
%o (PARI) N=75; x='x+O('x^N); Vec( 1/prod(n=1, N, 1-moebius(2*n-1)^2*x^(2*n-1) ) )
%K nonn
%O 0,4
%A _Joerg Arndt_, Aug 27 2008