id:A099323 - OEIS Search Results

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Expansion of (sqrt(1+3x)+sqrt(1-x))/(2sqrt(1-x)).

+0
4

1, 1, 0, 1, -1, 3, -6, 15, -36, 91, -232, 603, -1585, 4213, -11298, 30537, -83097, 227475, -625992, 1730787, -4805595, 13393689, -37458330, 105089229, -295673994, 834086421, -2358641376, 6684761125, -18985057351, 54022715451, -154000562758, 439742222071, -1257643249140 (list; graph; listen)

	OFFSET	`0,6`
	COMMENT	`Binomial transform is A072100. Signed Motzkin numbers with an additional leading 1.`
	LINKS	`C. Banderier and D. Merlini, Lattice paths with an infinite set of jumps`
	FORMULA	`a(n)=0^n+sum{k=0..n-1, binomial(n-1, k)(-1)^k*C(k)}.`
	CROSSREFS	`Cf. A005043, A000108.` `Sequence in context: A033192 A126971 A005043 this_sequence A058534 A063778 A087124` `Adjacent sequences: A099320 A099321 A099322 this_sequence A099324 A099325 A099326`
	KEYWORD	`easy,sign`
	AUTHOR	`Paul Barry (pbarry(AT)wit.ie), Oct 12 2004`

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Last modified August 19 23:53 EDT 2008. Contains 142930 sequences.

AT&T Labs Research