A301777 - OEIS

%I #7 Mar 31 2018 06:53:35

%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