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A003267
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Central Fibonomial coefficients.
(Formerly M4272)
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1
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1, 1, 6, 60, 1820, 136136, 27261234, 14169550626, 19344810307020, 69056421075989160, 645693859487298425256, 15803204856220738696714416, 1012673098498882654470985390406, 169885799961166470686816475170920550
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| The largest prime factor of a(n): 1, 1, 3, 5, 13, 17, 89, 233, 233, 1597, 1597, 1597, 28657, 28657, 28657, 514229, 514229, 514229, 514229, 514229, 514229, 514229, 433494437, 433494437, 2971215073, ..., . The union of the above list is: 1, 3, 5, 13, 17, 89, 233, 1597, 28657, 514229, 433494437, 2971215073, 14736206161, 46165371073, 92180471494753, 99194853094755497, ..., . [From Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 04 2009]
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REFERENCES
| A. Brousseau, A sequence of power formulas, Fib. Quart., 6 (1968), 81-83.
A. Brousseau, Fibonacci and Related Number Theoretic Tables. Fibonacci Association, San Jose, CA, 1972, p. 74.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Eric Weisstein's World of Mathematics, Central Fibonomial Coefficient [From Eric W. Weisstein (eric(AT)weisstein.com), Dec 08 2009]
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FORMULA
| a(n)=(-1)^floor(n/2)*det(M(n, -1))/det(M(n, 0)) where M(n, m) is the n X n matrix with coefficient 1/F(i+j+m) - Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 05 2004
a(n) = -(GoldenRatio^n^2 QPochhammer[(-1)^n GoldenRatio^(-2 n), -GoldenRatio^-2, 1 + n])/((-1 + (-1)^n GoldenRatio^(-2 n)) QPochhammer[ -GoldenRatio^-2, -GoldenRatio^-2, n] [From Eric W. Weisstein (eric(AT)weisstein.com), Dec 08 2009]
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MAPLE
| with(combinat); a[n] := product(fibonacci(n+k), k=0..n-2)/product(fibonacci(k), k=1..n-1);
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MATHEMATICA
| f[n_] := Product[ Fibonacci[n + k]/Fibonacci[k + 1], {k, 0, n - 2}]; Array[ f, 14] [From Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 04 2009]
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PROG
| (PARI) a(n)=prod(k=0, n-2, fibonacci(n+k))/prod(k=1, n-1, fibonacci(k)) for(n=2, 14, print1(a(n), ", "))
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CROSSREFS
| Bisection of A003268. Cf. A008341.
Cf. A062381.
Sequence in context: A061573 A092356 A001416 * A010574 A082681 A061431
Adjacent sequences: A003264 A003265 A003266 * A003268 A003269 A003270
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Sascha Kurz (sascha.kurz(AT)uni-bayreuth.de) and Rick L. Shepherd (rshepherd2(AT)hotmail.com), Mar 24 2002
a(1) = 1 added by N. J. A. Sloane, Dec 06 2009
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