%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