A294809 Expansion of Product_{k>=1} (1 - k^k*x^k)^k.

1, -1, -8, -73, -927, -13969, -254580, -5288596, -124795126, -3272571133, -94692028369, -2991756529687, -102571647087930, -3791499758414848, -150359326161180392, -6367668575791613601, -286854342016830115157, -13697147209040205869792

Offset: 0

Author

Seiichi Manyama, Nov 09 2017

Keywords

• sign

Comments

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

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..385

Crossrefs

Column k=1 of A294808.

Cf. A294810.

Programs

PARI

N=66; x='x+O('x^N); Vec(prod(k=1, N, (1-k^k*x^k)^k))

Formula

a(0) = 1 and a(n) = -(1/n) * Sum_{k=1..n} A294810(k)*a(n-k) for n > 0.