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A295245 Expansion of Product_{k>=1} 1/(1 + k^k*x^k)^k. 2

%I

%S 1,-1,-7,-74,-902,-14075,-253551,-5307194,-124832925,-3278747898,

%T -94780240390,-2995303153545,-102658540155454,-3794631664471440,

%U -150460754913170964,-6371573878247136298,-287006135162339175131,-13703650554585427586271

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

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

%H Seiichi Manyama, <a href="/A295245/b295245.txt">Table of n, a(n) for n = 0..385</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^(2+n)*(-1)^(n/d).

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

%Y Cf. A266964, A294813, A295244.

%K sign

%O 0,3

%A _Seiichi Manyama_, Nov 18 2017

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Last modified May 29 01:41 EDT 2022. Contains 354122 sequences. (Running on oeis4.)