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A303306
Expansion of Product_{n>=1} ((1 - (2*x)^n)/(1 + (2*x)^n))^(1/2).
7
1, -2, -2, -4, 6, 4, 12, 56, 134, -108, 196, 328, -484, -88, -3752, -18576, 16838, -16460, -95340, -24408, -201036, -472584, 565544, 1424144, 1843356, -6632568, 10365224, 2317008, 49620088, 130484688, -4419664, 631241440, 761908550, -29690892, 329427380, -8889717144, 23673793860
OFFSET
0,2
LINKS
FORMULA
a(0) = 1 and a(n) = -(1/n) * Sum_{k=1..n} 2^(k-1) * A054785(k) * a(n-k) for n > 0.
PROG
(Ruby)
def s(n)
s = 0
(1..n).each{|i| s += i if n % i == 0}
s
end
def A303306(n)
ary = [1]
a = (0..n).map{|i| 2 ** (i - 1) * (s(2 * i) - s(i))}
(1..n).each{|i| ary << -(1..i).inject(0){|s, j| s + a[j] * ary[-j]} / i}
ary
end
p A303306(100)
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Apr 21 2018
STATUS
approved