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A075377
Triangle read by rows in which n-th row gives all values of n!/{(p!)^a*(q!)^b*(r!)^c*...} (in increasing order) for all factorizations n = p^a*q^b*r^c*....
0
1, 1, 1, 1, 6, 1, 1, 60, 1, 1, 840, 5040, 1, 10080, 1, 15120, 1, 1, 332640, 3326400, 19958400, 1, 1, 8648640, 1, 1816214400, 1, 259459200, 36324288000, 217945728000, 1307674368000, 1, 1, 8821612800, 1482030950400, 88921857024000, 1, 1
OFFSET
1,5
COMMENTS
This is a modification of A036038.
A001055 gives the row lengths. - David Wasserman, Jan 17 2005
REFERENCES
Amarnath Murthy, Generalization of partition function,Introducing Smarandache Factor Partition, Smarandache Notions Journal, Vol. 11, 2000.
EXAMPLE
The row for n = 12 is: 1, 332640, 3326400, 19958400, since 12 = 12, 6*2, 4*3, 3*2*2.
Triangle begins:
1
1
1
1 6
1
1 60
1
1 840 5040
1 10080
1 15120
1
1 332640 3326400 19958400
1
1 8648640
1 1816214400
1 259459200 36324288000 217945728000 1307674368000
1
1 8821612800 1482030950400 88921857024000
1
1 335221286400 844757641728000 5068545850368000
CROSSREFS
KEYWORD
tabf,nonn
AUTHOR
Amarnath Murthy, Sep 21 2002
EXTENSIONS
More terms from David Wasserman, Jan 17 2005
STATUS
approved