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A145107
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Coefficients of q-series of numerator arising in a Hilbert series in works of Luque-Thibon.
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0
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1, 7, 220, 2606, 24229, 169840, 951944, 4391259, 17128360, 57582491, 169556652, 442817680, 1036416952, 2192191607, 4219669696, 7433573145, 12041305271, 18003453305, 24921751416, 32017113319, 38243274851, 42524815013
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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.
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LINKS
| Adriano Garsia, Gregg Musiker, Nolan Wallach, Guoce Xin, Invariants, Kronecker Products and Combinatorics of Some Remarkable Diophantine Systems (Extended Version) arXiv:0810.0060 [math.CO]
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EXAMPLE
| 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.
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CROSSREFS
| Sequence in context: A193186 A114939 A193224 * A140018 A202655 A009488
Adjacent sequences: A145104 A145105 A145106 * A145108 A145109 A145110
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KEYWORD
| fini,nonn,uned
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Oct 02 2008
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EXTENSIONS
| Replaced link to cached arXiv URL by link to the abstract - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 01 2010
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