A093423 Consider the triangle whose first part is shown as an example in the entry A093422. If the n-th term of the triangle read by rows is a fraction then a(n) is the denominator of the fraction, otherwise a(n)=1.

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

Offset: 1

Author

Amarnath Murthy, Mar 30 2004

Keywords

• nonn
• tabl
• frac

Examples

			Triangle begins:
  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;
  ...
		

Links

• G. C. Greubel, Rows n=1..100 of triangle, flattened

Crossrefs

Cf. A093412, A093413, A093414, A093415, A093417, A093418, A093419, A093420, A093421, A093422.

Programs

Magma

/* as a triangle */ [[Denominator(2*Binomial(n,k)*Factorial(k-1)/(2*n-k+1)): k in [1..n]]: n in [1..30]]; // G. C. Greubel, Sep 01 2018

Maple

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, Apr 28 2007

Mathematica

Table[Denominator[2*Binomial[n,k]*(k-1)!/(2*n-k+1)], {n,1,30}, {k,1,n}]//Flatten (* G. C. Greubel, Sep 01 2018 *)

PARI

for(n=1,10, for(k=1,n, print1(denominator(2*binomial(n,k)*(k-1)!/(2*n-k+1)), ", "))) \\ G. C. Greubel, Sep 01 2018

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

Extensions

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

Better definition from Omar E. Pol, Jan 10 2009