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

1,4

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.

Links

Table of n, a(n) for n=1..67.

Formula

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

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

Example

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).

Sequence in context: A119502 A142156 A136707 * A085826 A112477 A156984

Adjacent sequences: A179969 A179970 A179971 * A179973 A179974 A179975

Keyword

nonn,tabf

Author

Alford Arnold, Aug 04 2010

Status

approved