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Search: id:A093423
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| A093423 |
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In the following triangle the n-th row contains rational numbers in reduced form n/1, {n*(n-1)}/{n +(n-1)}, {(n)*(n-1)*(n-2)}/{n +(n-1)+(n-2)},...the last term is 2*(n-1)!/(n+1). 1 2 2/3 3 6/5 1 4 12/7 8/3 12/5 5 20/9 5 60/7 8 ... Sequence contains the denominator of the terms of rows. |
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| 1, 1, 3, 1, 5, 1, 1, 7, 3, 5, 1, 9, 1, 7, 1, 1, 11, 1, 1, 1, 7, 1, 13, 3, 11, 5, 3, 1, 1, 15, 1, 13, 1, 11, 1, 1, 1, 17, 1, 5, 1, 13, 1, 11, 1, 1, 19, 3, 17, 1, 1, 7, 13, 1, 11, 1, 21, 1, 19, 1, 17, 1, 1, 1, 13, 1, 1, 23, 1, 7, 5, 19, 1, 17, 1, 1, 1, 13
(list; table; graph; listen)
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OFFSET
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1,3
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FORMULA
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A093422(n,m)/A093423(n,m) = 2*binomial(n,m)*(m-1)!/(2*n-m+1) for 2<=m<n. A093422(n,1)/A093423(n,1)= n. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 28 2007
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MAPLE
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A09342x := proc(n, m) local a, i, N, D ; N := n ; if m = 1 then D := 1 ; else D := n ; end ; for i from 1 to m-1 do N := N*(n-i) ; D := D+n-i ; od ; simplify(N/D) ; end: A093423 := proc(n, m) denom(A09342x(n, m)) ; end: for n from 1 to 12 do for m from 1 to n do printf("%d, ", A093423(n, m)) ; od ; od ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 28 2007
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CROSSREFS
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Cf. A093412, A093413, A093414, A093415, A093417, A093418, A093419, A093420, A093421, A093422.
Sequence in context: A094919 A010286 A002945 this_sequence A134700 A085407 A016475
Adjacent sequences: A093420 A093421 A093422 this_sequence A093424 A093425 A093426
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KEYWORD
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more,nonn,tabl,frac,uned,obsc
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Mar 30 2004
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 28 2007
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