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%I #14 Dec 25 2016 20:33:04
%S 1,2,4,6,9,13,18,24,32,42,54,69,87,109,136,168,206,252,306,370,446,
%T 535,639,761,903,1068,1260,1482,1738,2034,2374,2764,3212,3724,4309,
%U 4977,5737,6601,7583,8696,9956,11382,12992,14808,16856
%N Number of sums S of distinct positive integers satisfying S <= n.
%H Vaclav Kotesovec, <a href="/A026906/b026906.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) ~ exp(Pi*sqrt(n/3)) * 3^(1/4) / (2*Pi*n^(1/4)) * (1 + (18+13*Pi^2) / (48*Pi*sqrt(3*n))). - _Vaclav Kotesovec_, Oct 25 2016
%F a(n) = A036469(n) - 1. - _Vaclav Kotesovec_, Oct 26 2016
%F G.f.: -1/(1 - x) + (1/(1 - x))*Product_{k>=1} (1 + x^k). - _Ilya Gutkovskiy_, Dec 25 2016
%e G.f. = x + 2*x^2 + 4*x^3 + 6*x^4 + 9*x^5 + 13*x^6 + 18*x^7 + 24*x^8 + 32*x^9 + ...
%t Table[ Sum[ PartitionsQ[k], {k, 1, n}], {n, 1, 50}]
%Y Partial sums of A000009.
%Y Cf. A000070.
%K nonn
%O 1,2
%A _Clark Kimberling_
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