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Search: id:A055392
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| A055392 |
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Number of bracketings of 0#0#0#...#0 giving result 0, where 0#0 = 1, 0#1 = 1#0 = 1#1 = 0. |
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+0
5
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| 1, 0, 2, 1, 12, 14, 100, 180, 990, 2310, 10920, 30030, 129612, 396576, 1620168, 5318841, 21029580, 72364578, 280735884, 997356360, 3828988020, 13905563100, 53108050320, 195875639310, 746569720572, 2784329809344, 10610782107800
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Operation # can be interpreted as NOT OR. The ratio a(n)/A000108(n-1) converges to sqrt(3)/3. Thanks to Soren Galatius Smith
Essentially second column of A112519. - Paul Barry (pbarry(AT)wit.ie), Sep 09 2005
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FORMULA
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G.f.: 1/2 + 1/2 (3 - 2 (1 - 4 x)^{1/2})^{1/2}
The g.f. Z is also given by Z(x) = C(x)U(xC(x)), where U(x) = C(-x) and C is the g.f. of the Catalan numbers. - Douglas Rogers, Oct 20 2005
a(n)=sum{j=0..n, (1/n)*(-1)^(n-1)*C(2n-j-1, n-j)*C(2(j-1), j-1)}; - Paul Barry (pbarry(AT)wit.ie), Sep 09 2005
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MATHEMATICA
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CoefficientList[ Series[1/2 + 1/2(3 - 2(1 - 4x)^(1/2))^(1/2), {x, 0, 27}], x] (from Robert G. Wilson v May 04 2004)
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CROSSREFS
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Cf. A055113, A055395.
Sequence in context: A048854 A151508 A164826 this_sequence A045873 A110060 A061081
Adjacent sequences: A055389 A055390 A055391 this_sequence A055393 A055394 A055395
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KEYWORD
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nonn
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AUTHOR
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Jeppe Stig Nielsen (sequence(AT)jeppesn.dk), Jun 24 2000
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