%I A110553
%S A110553 9,284,3004,19078
%N A110553 Column 12 of an array illustrated in A089584 and related to A034261.
%C A110553 The column sequences can also be calculated using sequences which map 
               to associated partitions. For example, 4 32 132 392 ... maps to 5+5+5+4 
               (n=19) and sequence 5 50 245 840 ... maps to 4+4+4+4+3. Many partitions 
               map to the same sequences since the mapping depends only on the "degree" 
               of the partition. In the above two cases, the degrees are 31 and 
               41 respectively. At n = 20 the relevant degrees are: 21,31,211,311,
               22,221,42,212,321,24 and 61. The associated partitions can be permuted 
               with the number of ways as indicated: 3 4 12 20 6 30 15 30 60 15 
               and 7 ways. Adding these values with the 32 and 50 ways from our 
               first two sequences confirms that A110553(2) = 284.
%e A110553 An examination of the relevant ordered gaussian polynomials reveals the 
               following distributions:
%e A110553 5 4
%e A110553 7 120 120 34 3
%e A110553 112 1127 1190 470 96 9
%e A110553 882 6692 7147 3270 910 162 15
%e A110553 therefore the sequence begins
%e A110553 9
%e A110553 284
%e A110553 3004
%e A110553 19078
%e A110553 ...
%Y A110553 Cf. A109821.
%Y A110553 Sequence in context: A119408 A012234 A012141 this_sequence A118893 A078326 
               A055792
%Y A110553 Adjacent sequences: A110550 A110551 A110552 this_sequence A110554 A110555 
               A110556
%K A110553 nonn
%O A110553 0,1
%A A110553 Alford Arnold (Alford1940(AT)aol.com), Jul 29 2005