A295245 Expansion of Product_{k>=1} 1/(1 + k^k*x^k)^k.

1, -1, -7, -74, -902, -14075, -253551, -5307194, -124832925, -3278747898, -94780240390, -2995303153545, -102658540155454, -3794631664471440, -150460754913170964, -6371573878247136298, -287006135162339175131, -13703650554585427586271

Offset: 0

Author

Seiichi Manyama, Nov 18 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

Cf. A266964, A294813, A295244.

Programs

PARI

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

Formula

a(0) = 1 and a(n) = (1/n) * Sum_{k=1..n} b(k)*a(n-k) where b(n) = Sum_{d|n} d^(2+n)*(-1)^(n/d).