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
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..386
Programs
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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
Comments