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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

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

Cf. A054785, A303307, A303343.

Sequence in context: A208314 A078099 A264872 * A118960 A107797 A316788

Adjacent sequences:  A303303 A303304 A303305 * A303307 A303308 A303309

KEYWORD

sign

AUTHOR

Seiichi Manyama, Apr 21 2018

STATUS

approved

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Last modified February 25 14:40 EST 2021. Contains 341609 sequences. (Running on oeis4.)