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Search: id:A166587
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A166587 A signed variant of the Motzkin numbers. +0
2
1, 1, -1, 2, -4, 9, -21, 51, -127, 323, -835, 2188, -5798, 15511, -41835, 113634, -310572, 853467, -2356779, 6536382, -18199284, 50852019, -142547559, 400763223, -1129760415, 3192727797, -9043402501, 25669818476, -73007772802 (list; graph; listen)
OFFSET

0,4

COMMENT

Hankel transform is A131713. Binomial transform is A166588.

FORMULA

G.f.: (1+3x-sqrt(1+2x-3x^2))/(2x); (1+3x)/(1+2x-x^2/(1+x-x^2/(1+x-x^2/(1+x-x^2/(1+... (continued fraction).

a(n)=0^n+sum{k=0..n, C(n-1,k-1)*(-3)^(n-k)*A000108(k)}.

CROSSREFS

Sequence in context: A094286 A094287 A094288 this_sequence A086246 A001006 A027057

Adjacent sequences: A166584 A166585 A166586 this_sequence A166588 A166589 A166590

KEYWORD

easy,sign

AUTHOR

Paul Barry (pbarry(AT)wit.ie), Oct 17 2009

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Last modified November 23 17:09 EST 2009. Contains 167438 sequences.


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