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A073155
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Left-most column sequence of triangle A073153.
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4
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1, 1, 4, 14, 56, 237, 1046, 4762, 22198, 105430, 508384, 2482297, 12248416, 60980875, 305955356, 1545397464, 7852100294, 40105277640, 205798130604, 1060467961508, 5485199090812, 28469067353686, 148220323891460
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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REFERENCES
| N. S. S. Gu, N. Y. Li and T. Mansour, 2-Binary trees: bijections and related issues, Discr. Math., 308 (2008), 1209-1221.
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FORMULA
| Convolution of sequence formed from sum of adjacent terms yields the original sequence minus the first term: a(n+1)=sum{k=0..n} [a(k)+a(k-1)]* [a(n-k)+a(n-k-1)], where a(-1)=0.
G.f.: 1/2*(1-(1-4*x*(1+x)^2)^(1/2))/x/(1+x)^2. - Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 10 2003
a(n)=sum{k=0..n, C(2k,n-k)*C(k)} - Paul Barry (pbarry(AT)wit.ie), Jul 09 2006
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EXAMPLE
| a(3)=a(0)*[a(2)+a(1)]+[a(1)+a(0)]*[a(1)+a(0)]+[a(2)+a(1)]*a(0) =1*[4+1] + [1+1]*[1+1] + [4+1]*1 = 5 + 2*2 + 5 = 14.
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CROSSREFS
| Cf. A073153, A073156, A073157.
Sequence in context: A143406 A132837 A149491 * A006212 A126701 A151884
Adjacent sequences: A073152 A073153 A073154 * A073156 A073157 A073158
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KEYWORD
| easy,nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Jul 29 2002
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EXTENSIONS
| More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 10 2003
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