A303306 - OEIS

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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 (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.)