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Main diagonal of A283272.
5

%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