A307504 Expansion of Product_{k>=1} 1/(1-x^k)^((-1)^k*k^k).

1, -1, 4, -31, 293, -3499, 51284, -891276, 17928335, -409921846, 10500040633, -297796771914, 9262574642871, -313459274848233, 11464944476563718, -450647901022275715, 18943108018829605740, -847933752191806388254, 40266301788890216414608, -2021846883773977115156632

Offset: 0

Author

Seiichi Manyama, Apr 11 2019

Keywords

• sign

Comments

This sequence is obtained from the generalized Euler transform in A266964 by taking f(n) = (-1)^n * n^n, g(n) = 1.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..386

Crossrefs

Cf. A023880, A266964, A307497.

Programs

Mathematica

nmax=20; CoefficientList[Series[Product[1/(1-x^k)^((-1)^k*k^k), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 12 2019 *)

PARI

N=20; x='x+O('x^N); Vec(1/prod(k=1, N, (1-x^k)^((-1)^k*k^k)))

Formula

a(n) ~ (-1)^n * n^n * (1 + exp(-1)/n + (exp(-1)/2 + 4*exp(-2))/n^2). - Vaclav Kotesovec, Apr 12 2019