A138533 Resort the multinomial sequence A036038 by source partition as described in A126442, A129306 and A136101.

1, 2, 1, 6, 3, 1, 24, 12, 4, 1, 6, 120, 60, 20, 5, 1, 30, 10, 720, 360, 120, 30, 6, 1, 180, 60, 15, 20, 90

Offset: 1

Author

Alford Arnold, Mar 27 2008

Keywords

• nonn
• tabf

Comments

Multinomials count permutations of multisets and also paths in lattices; for example, there are six paths (from null to full) through the lattice of divisors for signature 36: 2233 2323 2332 3223 3232 and 3322.

Examples

			a(11) is six because the eleventh least prime signature in source format is 36 the signature for partition 2+2 the ninth partition and A036038(9) = 6.
The tables begin:
1.......2.......6.......24......120.....720....5040.....40320......362880
........1.......3.......12.......60.....360....2520.....20160......181440
................1.......4........20.....120.....840......6720.......60480
........................1........5.......30.....210......1680.......15120
.. ..............................1........6......42......336........3024
..........................................1.......7.......56.........504
..................................................1........8..........72
...........................................................1...........9
.......................................................................1
........................6........30.....180....1260....10080........90720
.................................10......60.....420.....3360........30240
...
		

Crossrefs

Cf. A000142 A001710 A005651 (column sums) A025487 A053445.

Cf. A173333. [From Reinhard Zumkeller, Feb 19 2010]