A112360 Triangle read by rows: T(n,k) is the LCM of all C(n,k) integers from 1 + C(n,0) + C(n,1) + ... + C(n,k-1) to C(n,0) + C(n,1) + ... + C(n,k) (0 <= k <= n).

1, 1, 2, 1, 6, 4, 1, 12, 210, 8, 1, 60, 27720, 5460, 16, 1, 60, 720720, 13385572200, 3398220, 32, 1, 420, 232792560, 219060189739591200, 60218289392461200, 4076731260, 64, 1, 840, 2329089562800, 1182266884102822267511361600

Offset: 0

Author

Amarnath Murthy, Sep 07 2005

Keywords

• easy
• nonn
• tabl

Comments

Column 1 yields A003418. a(n,n) = 2^n. - Emeric Deutsch, Feb 03 2006

Examples

			Triangle begins:
  1;
  1,  2;
  1,  6,     4;
  1, 12,   210,    8;
  1, 60, 27720, 5460, 16;
  ...
The row for n = 3 is
1....3..........3.......1
1 lcm(2*3*4) lcm(5*6*7) 8 ====> 1 12 210 8.
		

Crossrefs

Cf. A112356, A112357, A112358, A112359.

Programs

Maple

T:=proc(n,k) if n=0 and k=0 then 1 else lcm(seq(j,j=1+sum(binomial(n,i),i=0..k-1)..sum(binomial(n,i),i=0..k))) fi end: for n from 0 to 7 do seq(T(n,k),k=0..n) od; # yields sequence in triangular form - Emeric Deutsch, Feb 03 2006

Extensions

More terms from Emeric Deutsch, Feb 03 2006