%I #24 Oct 24 2018 02:33:26
%S 1,-1,-4,-19,-55,5179,408149,23366098,-2659962750,-2946880278857,
%T -1715161696081878,603927037021100215,9904716216487281046207,
%U 52286804207990141325901614,-71925062774291844591785748425,-17522340813140430159774329947096591
%N Main diagonal of A283272.
%H Seiichi Manyama, <a href="/A283333/b283333.txt">Table of n, a(n) for n = 0..80</a>
%F a(n) = [x^n] Product_{k=1..n} (1 - x^k)^(k^n). - _Ilya Gutkovskiy_, Mar 06 2018
%o (Ruby)
%o require 'prime'
%o def power(a, n)
%o return 1 if n == 0
%o k = power(a, n >> 1)
%o k *= k
%o return k if n & 1 == 0
%o return k * a
%o end
%o def sigma(x, i)
%o sum = 1
%o pq = i.prime_division
%o if x == 0
%o pq.each{|a, n| sum *= n + 1}
%o else
%o pq.each{|a, n| sum *= (power(a, (n + 1) * x) - 1) / (power(a, x) - 1)}
%o end
%o sum
%o end
%o def A(k, m, n)
%o ary = [1]
%o s_ary = [0] + (1..n).map{|i| sigma(k, i * m)}
%o (1..n).each{|i| ary << (1..i).inject(0){|s, j| s - ary[-j] * s_ary[j]} / i}
%o ary
%o end
%o def A283333(n)
%o (0..n).map{|i| A(i + 1, 1, i)[-1]}
%o end
%Y Cf. A283272.
%K sign
%O 0,3
%A _Seiichi Manyama_, Mar 04 2017