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A047665
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Main diagonal of square array defined in A047662.
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5
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1, 6, 31, 160, 841, 4494, 24319, 132864, 731281, 4048726, 22523359, 125797984, 704966809, 3961924126, 22321190911, 126027618304, 712917362209, 4039658528934, 22924714957471, 130271906898720, 741188107113961, 4221707080583086
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n) = total number of weak plateaus in all Schroeder n-paths. A weak plateau is a subpath of the form UFF..FD where there are 0 or more Fs. For example, a(2)=6 counts the following weak plateaus (in parentheses) in the 6 Schroeder 2-paths: (UFD), U(UD)D, FF, (UD)F, F(UD), (UD)(UD). - David Callan (callan(AT)stat.wisc.edu), Aug 16 2006
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FORMULA
| G.f. = [1/sqrt(1-6z+z^2)-1/(1-z)]/2. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 25 2003
a(n) = sum( binomial(2*j-1, j-1) * binomial(n+j, 2*j), j, 1, n) - Stefan Hollos (stefan(AT)exstrom.com), Jul 21 2004
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MAPLE
| seq(add(multinomial(n+k, n-k, k, k)/2, k=1..n), n=1..22); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 18 2006
a:=n->sum(sum(binomial(n, j)*binomial(n, k)*binomial(k, j), j=0..n), k=1..n): seq(a(n)/2, n=1..22); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 02 2007
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CROSSREFS
| 2*a(n)+1 = A001850(n).
a(n)=sum(k=0..n l=0..n T(k, l)), array T as in A008288.
Sequence in context: A077352 A038223 A022034 * A003128 A058146 A015449
Adjacent sequences: A047662 A047663 A047664 * A047666 A047667 A047668
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KEYWORD
| nonn
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AUTHOR
| D. E. Knuth, N. J. A. Sloane (njas(AT)research.att.com).
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