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%I
%S 1,1,7,20,69,178,571,1451,4108,10480,27578,68401,172818,417979,
%T 1017575,2410964,5702481,13228877,30573978,69594694,157597162,
%U 352694078,784615466,1728604925,3785636280,8221695626,17751593170,38051212654,81103710142,171757084527
%N Expansion of Product_{k>=1} (1 + x^k)^A001001(k).
%H Vaclav Kotesovec, <a href="/A301777/b301777.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) ~ exp(2*Pi^(3/2) * (7*Zeta(3))^(1/4) * n^(3/4) / (3^(3/2) * 5^(1/4)) - 3*sqrt(5*Zeta(3)*n) / (4*7^(1/2)*Pi) + (sqrt(Pi) * 5^(1/4) / (3^(3/2) * (7*Zeta(3))^(1/4)) - 3^(5/2) * 5^(5/4) * Zeta(3)^(3/4) / (7^(5/4) * Pi^(7/2))) * n^(1/4) / 16 + 5/(448*Pi^2) - 675*Zeta(3) / (784*Pi^6)) * Pi^(1/4) * (7*Zeta(3))^(1/8) / (4*3^(1/4) * 5^(1/8) * n^(5/8)). - _Vaclav Kotesovec_, Mar 26 2018
%t nmax = 40; CoefficientList[Series[Exp[Sum[-(-1)^j * Sum[Sum[d*DivisorSigma[1, d], {d, Divisors[k]}] * x^(j*k) / j, {k, 1, Floor[nmax/j] + 1}], {j, 1, nmax}]], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Mar 31 2018 *)
%Y Cf. A001001, A226313.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Mar 26 2018
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