A283333 Main diagonal of A283272.

1, -1, -4, -19, -55, 5179, 408149, 23366098, -2659962750, -2946880278857, -1715161696081878, 603927037021100215, 9904716216487281046207, 52286804207990141325901614, -71925062774291844591785748425, -17522340813140430159774329947096591

Offset: 0

Author

Seiichi Manyama, Mar 04 2017

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..80

Crossrefs

Cf. A283272.

Programs

Ruby

require 'prime'
def power(a, n)
  return 1 if n == 0
  k = power(a, n >> 1)
  k *= k
  return k if n & 1 == 0
  return k * a
end
def sigma(x, i)
  sum = 1
  pq = i.prime_division
  if x == 0
    pq.each{|a, n| sum *= n + 1}
  else
    pq.each{|a, n| sum *= (power(a, (n + 1) * x) - 1) / (power(a, x) - 1)}
  end
  sum
end
def A(k, m, n)
  ary = [1]
  s_ary = [0] + (1..n).map{|i| sigma(k, i * m)}
  (1..n).each{|i| ary << (1..i).inject(0){|s, j| s - ary[-j] * s_ary[j]} / i}
  ary
end
def A283333(n)
  (0..n).map{|i| A(i + 1, 1, i)[-1]}
end

Formula

a(n) = [x^n] Product_{k=1..n} (1 - x^k)^(k^n). - Ilya Gutkovskiy, Mar 06 2018