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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*....
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%I #7 Dec 05 2013 19:55:37

%S 1,1,1,1,6,1,1,60,1,1,840,5040,1,10080,1,15120,1,1,332640,3326400,

%T 19958400,1,1,8648640,1,1816214400,1,259459200,36324288000,

%U 217945728000,1307674368000,1,1,8821612800,1482030950400,88921857024000,1,1

%N 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*....

%C This is a modification of A036038.

%C A001055 gives the row lengths. - _David Wasserman_, Jan 17 2005

%D Amarnath Murthy, Generalization of partition function,Introducing Smarandache Factor Partition, Smarandache Notions Journal, Vol. 11, 2000.

%e The row for n = 12 is: 1, 332640, 3326400, 19958400, since 12 = 12, 6*2, 4*3, 3*2*2.

%e Triangle begins:

%e 1

%e 1

%e 1

%e 1 6

%e 1

%e 1 60

%e 1

%e 1 840 5040

%e 1 10080

%e 1 15120

%e 1

%e 1 332640 3326400 19958400

%e 1

%e 1 8648640

%e 1 1816214400

%e 1 259459200 36324288000 217945728000 1307674368000

%e 1

%e 1 8821612800 1482030950400 88921857024000

%e 1

%e 1 335221286400 844757641728000 5068545850368000

%Y Cf. A036038, A001055, A036038.

%K tabf,nonn

%O 1,5

%A _Amarnath Murthy_, Sep 21 2002

%E More terms from _David Wasserman_, Jan 17 2005