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
KEYWORD
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