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A179972 Irregular table T(n,k)= A178886(n,k)/A048996(n,k) read by rows. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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

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Last modified August 18 20:02 EDT 2019. Contains 326109 sequences. (Running on oeis4.)