A307514 Expansion of Product_{k>=1} (1-x^k)^((-1)^k*k^k).

1, 1, -3, 24, -226, 2791, -42467, 761826, -15714798, 366401751, -9528266885, 273439284005, -8584541521286, 292695692569785, -10771202678289501, 425538242701632216, -17964593967281888258, 807094224863059707077, -38449142619220645357810, 1935991142823285710574298

Offset: 0

Author

Seiichi Manyama, Apr 12 2019

Keywords

• sign

Comments

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

Links

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

Crossrefs

Cf. A010054, A266964, A281781, A283499, A307460, A307497, A307504.

Programs

Mathematica

nmax=20; CoefficientList[Series[Product[(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(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 + 3*exp(-2))/n^2). - Vaclav Kotesovec, Apr 12 2019