A179972 Irregular table T(n,k) = A178886(n,k)/A048996(n,k) read by rows.

1, 1, 1, 2, 1, 1, 6, 2, 2, 1, 1, 24, 6, 6, 2, 2, 1, 1, 120, 24, 24, 24, 6, 6, 6, 2, 2, 1, 1, 720, 120, 120, 120, 24, 24, 24, 24, 6, 6, 6, 2, 2, 1, 1, 5040, 720, 720, 720, 720, 120, 120, 120, 120, 120, 24, 24, 24, 24, 24, 6, 6, 6, 2, 2, 1, 1, 40320

Offset: 1

Author

Alford Arnold, Aug 04 2010

Keywords

• nonn
• tabf

Comments

Row n has A000041(n) terms.

Consider the five partitions of the number 4:

4 3+1 2+2 2+1+1 and 1+1+1+1

rewriting as 4000 3100 2200 2110 and 1111

then a(n) counts the ways that the zeros can be permuted:

6,2,2,1,1

agreeing with the factorial of the difference between A036042 and A036043.

Examples

			Row four of A178886 begins: 6 4 2 3 1
Row four of A048996 begins: 1 2 1 3 1
so,
Row four of A179972 begins: 6 2 2 1 1
Triangle T(n,k) begins:
    1;
    1,  1;
    2,  1,  1;
    6,  2,  2,  1, 1;
   24,  6,  6,  2, 2, 1, 1;
  120, 24, 24, 24, 6, 6, 6, 2, 2, 1, 1;
  ...
		

Crossrefs

Cf. A178886, A048996, A036042, A036043, A179973 (row sums).

Formula

T(n,k) = ( A036042(n,k) - A036043(n,k))!.

T(n,k) = n!/A178888(n,k). - R. J. Mathar, Mar 03 2011