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%I #6 Apr 22 2019 18:06:30
%S 1,1,3,17,131,1239,14029,187627,2906553,50982929,993806531,
%T 21270277401,496425262123,12577053063847,344382608381421,
%U 10139294386051139,319175215666010609,10684742192933940897,378662321114852778883,14158327369578651838369,557151639159864934384851
%N Expansion of e.g.f. Product_{k>=1} (1 + x^k/(1 - x)^k)^(1/k).
%F E.g.f.: exp(Sum_{k>=1} A048272(k)*x^k/(k*(1 - x)^k)).
%F a(n) = Sum_{k=0..n} binomial(n-1,k-1)*A168243(k)*n!/k!.
%e E.g.f.: A(x) = 1 + x + 3*x^2/2! + 17*x^3/3! + 131*x^4/4! + 1239*x^5/5! + 14029*x^6/6! + 187627*x^7/7! + 2906553*x^8/8! + ...
%t nmax = 20; CoefficientList[Series[Product[(1 + x^k/(1 - x)^k)^(1/k), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
%t nmax = 20; CoefficientList[Series[Exp[Sum[Sum[(-1)^(d + 1), {d, Divisors[k]}] x^k/(k (1 - x)^k), {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!
%Y Cf. A048272, A129519, A168243, A307679, A320564.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Apr 21 2019
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