A295167 - OEIS

%I #15 Nov 18 2017 05:04:59

%S 1,-1,-1,-8,-50,-557,-6949,-108928,-1957445,-40752118,-952411952,

%T -24868752445,-715354102054,-22517233371562,-769323660770868,

%U -28367650033120436,-1122665826004076403,-47470796466768154403,-2135792162866000922808

%N Expansion of Product_{k>0} 1/(1 + k^k*x^k)^(1/k).

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

%H Seiichi Manyama, <a href="/A295167/b295167.txt">Table of n, a(n) for n = 0..387</a>

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

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

%Y Cf. A186633.

%K sign

%O 0,4

%A _Seiichi Manyama_, Nov 16 2017