%I A145107
%S A145107 1,7,220,2606,24229,169840,951944,4391259,17128360,57582491,169556652,
%T A145107 442817680,1036416952,2192191607,4219669696,7433573145,12041305271,
%U A145107 18003453305,24921751416,32017113319,38243274851,42524815013
%N A145107 Coefficients of q-series of numerator arising in a Hilbert series in 
               works of Luque-Thibon.
%C A145107 From formula (10) on p.4 of Garsia, Musiker, Wallach and Xin. This work 
               lies across three areas (in the title) of investigation that are 
               by themselves of independent interest. A problem that arose in quantum 
               computing led us to a link that tied these areas together. This link 
               consists of a single formal power series with a multifaced interpretation. 
               The deeper exploration of this link yielded results as well as methods 
               for solving some numerical problems in each of these separate areas.
%H A145107 Adriano Garsia, Gregg Musiker, Nolan Wallach, Guoce Xin, <a href="http:/
               /arxiv.org/PS_cache/arxiv/pdf/0810/0810.0060v1.pdf">Invariants, Kronecker 
               Products and Combinatorics of Some Remarkable Diophantine Systems 
               (Extended Version)</a> Oct 01, 2008.
%e A145107 N_5 = q^44 + 7q^43 + 220q^42 + 2606q^41 + 24229q^40 + 169840^q39 + 951944q^38 
               + 4391259q^37 + 17128360q^36 + 57582491q^35 + 169556652q^34 + 442817680q^33 
               + 1036416952q^32 + 2192191607q^31 + 4219669696q^30 + 7433573145q^29 
               + 12041305271q^28 + 18003453305q^27 + 24921751416q^26 + 32017113319q^25 
               + 38243274851q^24 + 42524815013q^23 + 44052440432q^22 + 42524815013q^21 
               + 38243274851q^20 + 32017113319q^19 + 24921751416q^18 + 18003453305q^17 
               + 12041305271q^16 + 7433573145q^15 + 4219669696q^14 + 2192191607q^13 
               + 1036416952q^12 + 442817680q^11 + 169556652q^10 + 57582491q^9 + 
               17128360q^8 + 4391259q^7 + 951944q^6 + 169840q^5 + 24229q^4 + 2606q^3 
               + 220q^2 + 7q + 1.
%Y A145107 Sequence in context: A045760 A046033 A114939 this_sequence A140018 A009488 
               A138247
%Y A145107 Adjacent sequences: A145104 A145105 A145106 this_sequence A145108 A145109 
               A145110
%K A145107 fini,nonn,uned
%O A145107 0,2
%A A145107 Jonathan Vos Post (jvospost3(AT)gmail.com), Oct 02 2008