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A026016
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Binomial(2*n-1, n) - binomial(2*n-1, n+3).
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3
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1, 3, 10, 34, 117, 407, 1430, 5070, 18122, 65246, 236436, 861764, 3157325, 11622015, 42961470, 159419670, 593636670, 2217608250, 8308432140, 31212003420, 117544456770, 443690433654, 1678353186780, 6361322162444, 24155384502452, 91882005146652
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Number of (s(0), s(1), ..., s(2n-1)) such that s(i) is a nonnegative integer and |s(i) - s(i-1)| = 1 for i = 1,2,...,n, s(0) = 2, s(2n-1) = 3. Also a(n) = T(2n-1,n-1), where T is the array defined in A026009.
Number of integer lattice paths from (0,2) to (n-1,n+2) that do not cross the main diagonal.
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FORMULA
| Expansion of (1+x^1*C^3)*C^2, where C = (1-(1-4*x)^(1/2))/(2*x) is g.f. for Catalan numbers, A000108.
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MAPLE
| c := n -> binomial(2*n, n)/(n+1):b := n -> if n<2 then 1; else c(n)-c(n-1); fi:a := n -> add(b(i)*c(n-i), i=1..n-1): > seq(a(n), n=2..27); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 10 2007
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CROSSREFS
| Cf. A026009.
Sequence in context: A059738 A094832 A071725 * A109263 A136439 A178578
Adjacent sequences: A026013 A026014 A026015 * A026017 A026018 A026019
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KEYWORD
| nonn
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
| Better description from Darko Marinov (marinov(AT)lcs.mit.edu), May 17 2001
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