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%I #14 May 25 2015 19:03:29
%S 1,0,0,0,0,0,1,0,1,1,3,2,5,4,8,8,13,13,21,21,31,33,46,49,67,72,95,104,
%T 134,146,186,203,253,279,343,378,461,507,611,675,806,889,1055,1163,
%U 1369,1512,1768,1950,2270,2502,2896,3193,3678,4051,4649,5117,5847
%N Number of partitions of n into distinct parts less than or equal to n/2.
%C Intuitively the sequence is asymptotic to A000009. a(300)/A000009(300) is approximately .997749.
%H Alois P. Heinz, <a href="/A258259/b258259.txt">Table of n, a(n) for n = 0..10000</a>
%F a(n) = [x^n] Product_{i=1..floor(n/2)} 1 + x^i.
%e a(9) = 1 because we have: 2+3+4.
%e a(10) = 3 because we have: 1+4+5, 2+3+5, 1+2+3+4.
%p b:= proc(n, i) option remember; local m; m:= i*(i+1)/2;
%p `if`(n>m, 0, `if`(n=m, 1, b(n, i-1)+`if`(i>n, 0, b(n-i, i-1))))
%p end:
%p a:= n-> b(n, iquo(n, 2)):
%p seq(a(n), n=0..60); # _Alois P. Heinz_, May 25 2015
%t Prepend[Table[nn = n;Coefficient[Series[Product[1 + x^i, {i, 1, nn/2}], {x, 0, nn}],x^n], {n, 1, 50}], 1]
%Y Cf. A000009.
%K nonn
%O 0,11
%A _Geoffrey Critzer_, May 24 2015
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