A137948 Triangle read by rows, A000012 * A136579.

1, 2, 1, 3, 2, 2, 4, 3, 4, 6, 5, 4, 6, 12, 24, 6, 5, 8, 18, 48, 120, 7, 6, 10, 24, 72, 240, 720, 8, 7, 12, 30, 96, 360, 1440, 5040, 9, 8, 14, 36, 120, 480, 2160, 10080, 40320, 10, 9, 16, 42, 144, 600, 2880, 15120, 80640, 362880

Offset: 0

Author

Gary W. Adamson, Feb 28 2008

Keywords

• nonn
• tabl

Comments

Row sums = A014144 starting (1, 3, 7, 17, 51, 205, ...).

T(n,k) = A245334(n,k) / A007318(n,k), 0 <= k <= n. - Reinhard Zumkeller, Aug 31 2014

Examples

			First few rows of the triangle:
  1;
  2, 1;
  3, 2,  2;
  4, 3,  4,  6;
  5, 4,  6, 12, 24;
  6, 5,  8, 18, 48, 120;
  7, 6, 10, 24, 72, 240, 720;
  ...
		

Links

• Reinhard Zumkeller, Rows n = 0..125 of triangle, flattened

Crossrefs

Cf. A136579, A014144.

Cf. A245334, A007318.

Programs

Haskell

a137948 n k = a137948_tabl !! n !! k
a137948_row n = a137948_tabl !! n
a137948_tabl = zipWith (zipWith div) a245334_tabl a007318_tabl
-- Reinhard Zumkeller, Aug 31 2014

Formula

As infinite lower triangular matrices, A000012 * A136579, where A000012 = (1; 1,1; 1,1,1; ...) and A136579 = (1; 1,1; 1,1,2; 1,1,2,6; 1,1,2,6,24; ...).

T(n,k) = (n+1-k) * k! for 0 <= k <= n. - Werner Schulte, Oct 06 2020

Extensions

Offset changed by Reinhard Zumkeller, Aug 31 2014