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Resort the multinomial sequence A036038 by source partition as described in A126442, A129306 and A136101.
4

%I #7 Apr 15 2015 05:26:56

%S 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,

%T 60,15,20,90

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

%C 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.

%e 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.

%e The tables begin:

%e 1.......2.......6.......24......120.....720....5040.....40320......362880

%e ........1.......3.......12.......60.....360....2520.....20160......181440

%e ................1.......4........20.....120.....840......6720.......60480

%e ........................1........5.......30.....210......1680.......15120

%e .. ..............................1........6......42......336........3024

%e ..........................................1.......7.......56.........504

%e ..................................................1........8..........72

%e ...........................................................1...........9

%e .......................................................................1

%e ........................6........30.....180....1260....10080........90720

%e .................................10......60.....420.....3360........30240

%e ...

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

%Y Cf. A173333. [From _Reinhard Zumkeller_, Feb 19 2010]

%K nonn,tabf

%O 1,2

%A _Alford Arnold_, Mar 27 2008