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Search: id:A111160
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| A111160 |
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G.f.: C - Z; where C is the g.f. for the Catalan numbers (A000108) and Z is the g.f. for A055113 with offset 0. |
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+0
3
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| 0, 1, 1, 4, 9, 31, 91, 309, 1009, 3481, 11956, 42065, 148655, 532039, 1915369, 6950452, 25357233, 93034813, 342888250, 1269246437, 4715945712, 17583623988, 65766726906, 246694006971, 927801717255, 3497918129001, 13217196871126, 50046561077947
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Expressible in terms of ballot numbers.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..200
Douglas Rogers, Comments on A1111160, A055113 and A006013
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FORMULA
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Let C := (1 - sqrt(1 - 4*x)) / (2*x), Z := (- 1/4 - (1/4)*(1 - 4*x)^(1/2) + (1/4)*(2 + 2*(1 - 4*x)^(1/2) + 12*x)^(1/2))/x; g.f. is W := C - Z.
G.f.: -((-3 + sqrt(1 - 4x) + sqrt(2)*sqrt(1 + sqrt(1 - 4x) + 6x))/(4x)).
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MATHEMATICA
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CoefficientList[ Series[ -((-3 + Sqrt[1 - 4*x] + Sqrt[2]*Sqrt[1 + Sqrt[1 - 4x] + 6x])/(4x)), {x, 0, 10}], x] (* Robert G. Wilson v *)
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CROSSREFS
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Cf. A055113, A006013.
Sequence in context: A042599 A145543 A141043 this_sequence A071378 A053192 A005985
Adjacent sequences: A111157 A111158 A111159 this_sequence A111161 A111162 A111163
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), following a suggestion from Douglas Rogers, Oct 22 2005
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