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A084076
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Length of list created by n substitutions k -> Range[ -1-Abs[k],Abs[k]+1] starting with {1}.
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4
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1, 5, 27, 157, 963, 6141, 40323, 270845, 1852419, 12857341, 90337283, 641286141, 4592533507, 33139654653, 240723001347, 1758796578813, 12916805074947, 95300512382973, 706044251602947, 5250379998560253, 39176121681444867
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 2*a(n-1) is the second diagonal of the triangle A115195.
Row sums of A167431. Hankel transform is A167435. [From Paul Barry (pbarry(AT)wit.ie), Nov 03 2009]
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FORMULA
| invOGF=-((1 + 5*n + 2*n^2 - (1 + 2*n)*Sqrt[1 + 6*n + n^2])/(4*n^2))
G.f.: 2*((c(2*x))^3)/(1+c(2*x)) with the o.g.f. c(x) of A000108 (Catalan numbers).
G.f.: (-1 + (1-x)*c(2*x))/(x*(1+x)) (W. Lang, Feb 23 2006, see A115139).
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EXAMPLE
| {{1}, {-2,-1,0,1,2},
{-3,-2,-1,0,1,2,3,-2,-1,0,1,2,-1,0,1,-2,-1,0,1,2,-3,-2,-1,0,1,2,3}
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MATHEMATICA
| Rest@CoefficientList[InverseSeries[Series[ -((1+5*n+2*n^2-(1+2*n)*Sqrt[1+6*n+n^2])/(4*n^2)), {n, 0, 28}]], n] or Length/@Flatten/@NestList[ # /. k_Integer :> Range[ -1-Abs[k], Abs[k]+1]&, {1}, 8]
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CROSSREFS
| Third column (m=2) of triangle A115193, called C(1, 2).
a(n)=sum(A115195(n, m), m=1..n+1), n>=0 (row sums of triangle).
Sequence in context: A052227 A101386 A153233 * A081924 A138772 A082425
Adjacent sequences: A084073 A084074 A084075 * A084077 A084078 A084079
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KEYWORD
| nonn
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AUTHOR
| Wouter Meeussen (wouter.meeussen(AT)pandora.be), May 11 2003
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