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 A301874 Expansion of Product_{k>=1} (1 + x^k)^A007437(k). 3

%I

%S 1,1,4,11,27,64,156,345,779,1706,3665,7742,16207,33300,67830,136526,

%T 271969,536588,1049801,2035620,3917547,7482738,14192358,26738962,

%U 50062081,93158467,172366532,317166618,580542738,1057269629,1916174666

%N Expansion of Product_{k>=1} (1 + x^k)^A007437(k).

%H Vaclav Kotesovec, <a href="/A301874/b301874.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) ~ exp(2*Pi * (7*Zeta(3))^(1/4) * n^(3/4) / (3^(5/4) * 5^(1/4)) + sqrt(15*Zeta(3)*n/7)/4 - (5^(1/4) * 7^(3/4) * Pi / (3^(7/4) * Zeta(3)^(1/4)) + 15^(5/4) * Zeta(3)^(3/4) / (7^(5/4)*Pi)) * n^(1/4)/16 + 75*Zeta(3) / (784*Pi^2) + 5/192) * (7*Zeta(3))^(1/8) / (2^(95/48) * 15^(1/8) * n^(5/8)).

%t nmax = 40; CoefficientList[Series[Exp[Sum[-(-1)^j * Sum[(DivisorSigma[1, k] + DivisorSigma[2, k]) * x^(j*k) / (2*j), {k, 1, Floor[nmax/j] + 1}], {j, 1, nmax}]], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Mar 31 2018 *)

%Y Cf. A007437, A301873.

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, Mar 28 2018

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Last modified April 3 13:32 EDT 2020. Contains 333197 sequences. (Running on oeis4.)