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

1, 1, 4, 11, 27, 64, 156, 345, 779, 1706, 3665, 7742, 16207, 33300, 67830, 136526, 271969, 536588, 1049801, 2035620, 3917547, 7482738, 14192358, 26738962, 50062081, 93158467, 172366532, 317166618, 580542738, 1057269629, 1916174666

Offset: 0

Author

Vaclav Kotesovec, Mar 28 2018

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A007437, A301873.

Programs

Mathematica

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 *)

Formula

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)).