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

%I A138533 #7 Apr 15 2015 05:26:56
%S A138533 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 A138533 60,15,20,90
%N A138533 Resort the multinomial sequence A036038 by source partition as described in A126442, A129306 and A136101.
%C A138533 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 A138533 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 A138533 The tables begin:
%e A138533 1.......2.......6.......24......120.....720....5040.....40320......362880
%e A138533 ........1.......3.......12.......60.....360....2520.....20160......181440
%e A138533 ................1.......4........20.....120.....840......6720.......60480
%e A138533 ........................1........5.......30.....210......1680.......15120
%e A138533 .. ..............................1........6......42......336........3024
%e A138533 ..........................................1.......7.......56.........504
%e A138533 ..................................................1........8..........72
%e A138533 ...........................................................1...........9
%e A138533 .......................................................................1
%e A138533 ........................6........30.....180....1260....10080........90720
%e A138533 .................................10......60.....420.....3360........30240
%e A138533 ...
%Y A138533 Cf. A000142 A001710 A005651 (column sums) A025487 A053445.
%Y A138533 Cf. A173333. [From _Reinhard Zumkeller_, Feb 19 2010]
%K A138533 nonn,tabf
%O A138533 1,2
%A A138533 _Alford Arnold_, Mar 27 2008