A301980 Expansion of Product_{k>=1} (1 + x^k)^A065958(k).

1, 1, 5, 15, 40, 106, 281, 685, 1690, 4050, 9496, 21908, 49902, 111740, 247465, 541353, 1171070, 2507602, 5319085, 11178947, 23298878, 48169708, 98834943, 201335651, 407345067, 818767703, 1635528657, 3247634227, 6412057831, 12590738729, 24593652845

Offset: 0

Author

Vaclav Kotesovec, Mar 30 2018

Keywords

• nonn

Links

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

Crossrefs

Cf. A065958, A156733, A301978.

Programs

Mathematica

nmax = 40; CoefficientList[Series[Exp[Sum[-(-1)^j * Sum[Sum[MoebiusMu[k/d]^2*d^2, {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 *)

Formula

a(n) ~ exp(2^(5/4) * sqrt(7) * Zeta(3)^(1/4) * n^(3/4) / sqrt(3*Pi) - sqrt(Pi) * n^(1/4) / (2^(9/4) * 3^(3/2) * sqrt(7) * Zeta(3)^(1/4))) * 21^(1/4) * Zeta(3)^(1/8) / (2^(15/8) * Pi^(3/4) * n^(5/8)).