A093422 -id:A093422 - cp's OEIS frontend

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

Amarnath Murthy, Mar 30 2004

			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;
  ...

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

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

/* 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

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

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 *)

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

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

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

Better definition from Omar E. Pol, Jan 10 2009

A093420 Triangle read by rows: T(n,k) is the numerator of f(n, k) = (Product_{i = 0..k-1} (n-i))/(Sum_{i = 1..k} i) for 1 <= k <= n.

Original entry on oeis.org

1, 2, 2, 3, 2, 1, 4, 4, 4, 12, 5, 20, 10, 12, 8, 6, 10, 20, 36, 48, 240, 7, 14, 35, 84, 168, 240, 180, 8, 56, 56, 168, 448, 960, 1440, 1120, 9, 24, 84, 1512, 1008, 2880, 6480, 10080, 8064, 10, 30, 120, 504, 2016, 7200, 21600, 50400, 80640, 725760, 11, 110, 165

Offset: 1

Amarnath Murthy, Mar 30 2004

			Triangle T(n,k) (with rows n >= 1 and columns k >= 1) begins as follows:
  1,
  2,  2,
  3,  2,  1,
  4,  4,  4, 12,
  5, 20, 10, 12,   8,
  6, 10, 20, 36,  48, 240,
  7, 14, 35, 84, 168, 240, 180;
  ...

Cf. A090585, A090586, A093412, A093421 (denominators), A093422.

T(n,n) = numerator(f(n, n)) = numerator(2*(n-1)!/(n+1)) = A090586(n).

Edited and extended by David Wasserman, Aug 29 2006

cp's OEIS Frontend

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.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Magma

Maple

Mathematica

PARI

Formula

Extensions