Search: id:A093422
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%I A093422
%S A093422 1,2,2,3,6,1,4,12,8,12,5,20,5,60,8,6,30,8,20,36,240,7,42,35,420,504,560,
%T A093422 180,8,56,16,840,224,6720,1152,1120,9,72,21,504,432,20160,4320,90720,
%U A093422 8064,10,90,80,2520,756,3360,86400,453600,67200,725760,11,110,33,3960
%N A093422 In the triangle shown below the n-th row contains n rational numbers 
               n/1, {n*(n-1)}/{n +(n-1)}, {(n)*(n-1)*(n-2)}/{n +(n-1)+(n-2)},..., 
               the last term being 2*(n-1)!/(n+1). Sequence gives the numerators 
               in each row.
%F A093422 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
%e A093422 Triangle of fractions starts
%e A093422 1,
%e A093422 2, 2/3,
%e A093422 3, 6/5, 1,
%e A093422 4, 12/7, 8/3, 12/5,
%e A093422 5, 20/9, 5, 60/7, 8,
%e A093422 6, 30/11, 8, 20, 36, 240/7,
%e A093422 7, 42/13, 35/3, 420/11, 504/5, 560/3, 180,
%e A093422 8, 56/15, 16, 840/13, 224, 6720/11, 1152, 1120,
%e A093422 9, 72/17, 21, 504/5, 432, 20160/13, 4320, 90720/11, 8064,
%p A093422 A09342x := proc(n,m) local 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: A093422 := proc(n,m) numer(A09342x(n,m)) 
               ; end: for n from 1 to 12 do for m from 1 to n do printf("%d, ",A093422(n,
               m)) ; od ; od ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 
               28 2007
%Y A093422 Cf. A093412, A093413, A093414, A093415, A093417, A093418, A093419, A093420, 
               A093421, A093423.
%Y A093422 Sequence in context: A099205 A051005 A002163 this_sequence A083506 A076333 
               A015051
%Y A093422 Adjacent sequences: A093419 A093420 A093421 this_sequence A093423 A093424 
               A093425
%K A093422 easy,frac,nonn,tabl
%O A093422 1,2
%A A093422 Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Mar 30 2004
%E A093422 More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 28 2007

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