OFFSET
1,2
LINKS
G. C. Greubel, Rows n=0..100 of triangle, flattened
FORMULA
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, Apr 28 2007
EXAMPLE
Triangle of fractions starts
1,
2, 2/3,
3, 6/5, 1,
4, 12/7, 8/3, 12/5,
5, 20/9, 5, 60/7, 8,
6, 30/11, 8, 20, 36, 240/7,
7, 42/13, 35/3, 420/11, 504/5, 560/3, 180,
8, 56/15, 16, 840/13, 224, 6720/11, 1152, 1120,
9, 72/17, 21, 504/5, 432, 20160/13, 4320, 90720/11, 8064,
MAPLE
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, Apr 28 2007
MATHEMATICA
Table[If[k == 1, n, Numerator[2*Binomial[n, k]*(k-1)!/(2*n-k+1)]], {n, 1, 30}, {k, 1, n}]//Flatten (* G. C. Greubel, Sep 01 2018 *)
PROG
(PARI) for(n=1, 10, for(k=1, n, print1(if(k==1, n, denominator(2*binomial(n, k)*(k-1)!/(2*n-k+1))), ", "))) \\ G. C. Greubel, Sep 01 2018
(Magma) /* as a triangle */ [[k le 1 select n else Numerator(2*Binomial(n, k)*Factorial(k-1)/(2*n-k+1)): k in [1..n]]: n in [1..10]]; // G. C. Greubel, Sep 01 2018
CROSSREFS
KEYWORD
AUTHOR
Amarnath Murthy, Mar 30 2004
EXTENSIONS
More terms from R. J. Mathar, Apr 28 2007
STATUS
approved