A134098 - OEIS

This site is supported by donations to The OEIS Foundation.

A134098

a(n) = 2^[n(n+1) - A000120(n)] * [x^n] (1+x)^(1/2^n) for n>=0, where A000120(n) = number of 1's in binary expansion of n.

1, 1, -3, 35, -7285, 1570863, -2762459931, 9861642254451, -1141290059372782605, 66806775363324062981915, -31603810290612531279241668449, 30166547730607848261858185370275389, -464256425980552239880944863449968127087425 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`0,3`
	COMMENTS	`[x^n] (1+x)^(1/2^n) denotes the coefficient of x^n in the (2^n)-root of (1+x), which has a denominator equal to 2^[n(n+1) - A000120(n)].`
	LINKS	`Table of n, a(n) for n=0..12.`
	EXAMPLE	`This sequence forms the numerators of coefficients [x^n] (1+x)^(1/2^n),` `where the denominators equal 2^b(n) and b(n) takes on values:` `[0,1,5,10,19,28,40,53,71,88,108,129,154,179,207,236,271,304,...],` `which is described by b(n) = n(n+1) - A000120(n) for n>=0.`
	PROG	`(PARI) {a(n)=polcoeff((1+x+xO(x^n))^(1/2^n), n)2^(n*(n+1)-subst(Pol(binary(n)), x, 1))}`
	CROSSREFS	`Cf. A000120; A134097 (variant); A134096.` `Sequence in context: A068002 A132557 A069954 * A132513 A034174 A119526` `Adjacent sequences: A134095 A134096 A134097 * A134099 A134100 A134101`
	KEYWORD	`sign`
	AUTHOR	`Paul D. Hanna, Oct 26 2007`
	STATUS	`approved`

Content is available under The OEIS End-User License Agreement .

Last modified May 23 23:31 EDT 2013. Contains 225613 sequences.