A303306 Expansion of Product_{n>=1} ((1 - (2*x)^n)/(1 + (2*x)^n))^(1/2).

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

Author

Seiichi Manyama, Apr 21 2018

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..3000

Crossrefs

Cf. A054785, A303307, A303343.

Programs

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)

Formula

a(0) = 1 and a(n) = -(1/n) * Sum_{k=1..n} 2^(k-1) * A054785(k) * a(n-k) for n > 0.