OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..80
FORMULA
a(n) = [x^n] Product_{k=1..n} (1 - x^k)^(k^n). - Ilya Gutkovskiy, Mar 06 2018
PROG
(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
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Mar 04 2017
STATUS
approved