

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
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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



