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A099323
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Expansion of (sqrt(1+3x)+sqrt(1-x))/(2sqrt(1-x)).
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9
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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
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OFFSET
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0,6
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COMMENTS
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Binomial transform is A072100. Signed Motzkin numbers with an additional leading 1.
Inverse binomial transform of A001405 gives this without the initial 1. So does the binomial transform of (-1)^n*A000108(n)=[1,-1,2,-5,14,-42,...]. - Philippe DELEHAM, Mar 20 2007
Contribution from Gary W. Adamson, Nov 09 2008: (Start)
Equals POLYMOTZKINT [1,-1,1,-1,...] signed (1, -1, 0, -1, -1, -3, -6,...).
Cf. A005717 for an example of the POLYMOTZKINT operation. (End)
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LINKS
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Table of n, a(n) for n=0..32.
C. Banderier and D. Merlini, Lattice paths with an infinite set of jumps
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FORMULA
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a(n)=0^n+sum{k=0..n-1, binomial(n-1, k)(-1)^k*C(k)}.
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CROSSREFS
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Cf. A005043, A000108.
Sequence in context: A033192 A174297 A005043 * A058534 A063778 A087124
Adjacent sequences: A099320 A099321 A099322 * A099324 A099325 A099326
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KEYWORD
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easy,sign
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AUTHOR
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Paul Barry, Oct 12 2004
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EXTENSIONS
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Edited by N. J. A. Sloane, Oct 05 2009
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STATUS
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approved
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