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

1,3

Links

G. C. Greubel, Rows n=1..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 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;
  ...

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 *)

Prog

(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
(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

Crossrefs

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

Sequence in context: A305444 A002945 A171232 * A326454 A227507 A134700

Adjacent sequences: A093420 A093421 A093422 * A093424 A093425 A093426

Keyword

nonn,tabl,frac

Author

Amarnath Murthy, Mar 30 2004

Extensions

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

Better definition from Omar E. Pol, Jan 10 2009

Status

approved