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%I #16 Nov 05 2017 08:07:26
%S 1,1,3,6,16,27,79,126,331,632,1436,2509,6800,11218,26044,51958,114941,
%T 205183,502228,875545,2027193,3963938,8389190,15504996,37555290,
%U 66502859,145809046,292860564,621638120,1156065731,2701045579
%N Expansion of Product_{k>0} (1-k^2*x^k)^(-1/k).
%H Seiichi Manyama, <a href="/A151954/b151954.txt">Table of n, a(n) for n = 0..3149</a>
%F a(0) = 1 and a(n) = (1/n) * Sum_{k=1..n} A073705(k)*a(n-k) for n > 0. - _Seiichi Manyama_, Nov 05 2017
%F From _Vaclav Kotesovec_, Nov 05 2017: (Start)
%F a(n) ~ c * 3^(2*n/3) / n^(2/3), where
%F c = 4.674336739118905298732313884863019... if mod(n,3)=0
%F c = 4.299861572054701010776554223312792... if mod(n,3)=1
%F c = 4.239106098573472870377481583112857... if mod(n,3)=2
%F (End)
%t nmax = 40; CoefficientList[Series[Product[(1-k^2*x^k)^(-1/k), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Nov 05 2017 *)
%Y Cf. A028342, A073705, A077335.
%K nonn
%O 0,3
%A _Franklin T. Adams-Watters_, Jul 03 2009
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