A307497 Expansion of Product_{k>=1} (1+x^k)^((-1)^k*k^k).

1, -1, 5, -32, 294, -3527, 51589, -894706, 17978610, -410803143, 10517824035, -298204099693, 9273022031794, -313755862498513, 11474175971184267, -450960476552715192, 18954545423649435646, -848383466771831169101, 40285210722052785437974

Offset: 0

Author

Seiichi Manyama, Apr 10 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. A083365, A261053, A266964, A284474, A307462.

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 + 5*exp(-2))/n^2). - Vaclav Kotesovec, Apr 12 2019