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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. 3
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, 180, 8, 56, 16, 840, 224, 6720, 1152, 1120, 9, 72, 21, 504, 432, 20160, 4320, 90720, 8064, 10, 90, 80, 2520, 756, 3360, 86400, 453600, 67200, 725760, 11, 110, 33, 3960 (list; table; graph; refs; listen; history; text; internal format)
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

Cf. A093412, A093413, A093414, A093415, A093417, A093418, A093419, A093420, A093421, A093423.

Sequence in context: A051005 A266583 A002163 * A297890 A083506 A248164

Adjacent sequences:  A093419 A093420 A093421 * A093423 A093424 A093425

KEYWORD

easy,frac,nonn,tabl

AUTHOR

Amarnath Murthy, Mar 30 2004

EXTENSIONS

More terms from R. J. Mathar, Apr 28 2007

STATUS

approved

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Last modified September 30 05:03 EDT 2020. Contains 337435 sequences. (Running on oeis4.)