|
%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
| 