1,2

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

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

...

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

Sequence in context: A103905 A103209 A089900 this_sequence A096334 A107867 A158442

Adjacent sequences: A138530 A138531 A138532 this_sequence A138534 A138535 A138536

nonn,tabf

Alford Arnold (Alford1940(AT)aol.com), Mar 27 2008