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A003150
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Fibonomial Catalan numbers.
(Formerly M3077)
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2
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1, 1, 3, 20, 364, 17017, 2097018, 674740506, 568965009030, 1255571292290712, 7254987185250544104, 109744478168199574282739, 4346236474244131564253156182, 450625464087974723307205504432150
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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REFERENCES
| Paul Barry, On Integer-Sequence-Based Constructions of Generalized Pascal Triangles, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.4.
H. W. Gould, A new primality criterion of Mann and Shanks and its relation to a theorem of Hermite with extension to Fibonomials, Fib. Quart., 10 (1972), 3550-364, 372.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..40
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FORMULA
| F(2n)F(2n-1)...F(n+2)/F(n)F(n-1)...F(1) = A010048(2*n,n)/F(n+1), F = Fibonacci numbers.
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EXAMPLE
| a(5)=F(10)...F(7)/F(5)...F(1)=55*34*21*13/5*3*2*1*1=17017.
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MAPLE
| A010048 := proc(n, k) local a, j ; a := 1 ; for j from 0 to k-1 do a := a*combinat[fibonacci](n-j)/combinat[fibonacci](k-j) ; end do: return a; end proc:
A003150 := proc(n) A010048(2*n, n)/combinat[fibonacci](n+1) ; end proc:
seq(A003150(n), n=0..20) ; # R. J. Mathar, Dec 06 2010
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MATHEMATICA
| f[n_] := f[n] = Fibonacci[n]; a[n_] := Product[f[k], {k, n+2, 2n}] / Product[f[k], {k, 1, n}]; Table[a[n], {n, 0, 13}] (* From Jean-François Alcover, Dec 14 2011 *)
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CROSSREFS
| Sequence in context: A163138 A201824 A203519 * A203194 A138897 A189603
Adjacent sequences: A003147 A003148 A003149 * A003151 A003152 A003153
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), H. W. Gould
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