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 A293943 Poincaré series for invariant polynomial functions on the space of binary forms of degree 24. 13
 1, 0, 1, 1, 5, 7, 29, 62, 201, 506, 1429, 3569, 9113, 21660, 50866, 114049, 250256, 530471, 1099354, 2215994, 4372347, 8429664, 15937900, 29540515, 53798630, 96288505, 169633646, 294284184, 503311347, 849051903, 1413975513, 2325798623, 3781205230, 6078784401, 9669020265, 15223385340 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Many of these Poincaré series has every other term zero, in which case these zeros have been omitted. LINKS Andries Brouwer, Poincaré Series (See n=24) EXAMPLE The Poincaré series is (1 + 3t^4 + 5t^5 + 22t^6 + 50t^7 + 161t^8 + 410t^9 + 1140t^10 + 2808t^11 + 6991t^12 + 16199t^13 + 36859t^14 + 80010t^15 + 169421t^16 + 346121t^17 + 689947t^18 + 1336028t^19 + 2528528t^20 + 4670438t^21 + 8449357t^22 + 14968148t^23 + 26025211t^24 + 44423184t^25 + 74560924t^26 + 123110049t^27 + 200201862t^28 + 320813495t^29 + 507041603t^30 + 790779399t^31 + 1217881983t^32 + 1853082547t^33 + 2787305828t^34 + 4146285473t^35 + 6102914802t^36 + 8891714037t^37 + 12828922109t^38 + 18335849747t^39 + 25970411969t^40 + 36463444967t^41 + 50766544654t^42 + 70106566677t^43 + 96055848819t^44 + 130611273929t^45 + 176294077526t^46 + 236260806268t^47 + 314440780906t^48 + 415686796764t^49 + 545958588510t^50 + 712520954002t^51 + 924180944791t^52 + 1191539827621t^53 + 1527289937061t^54 + 1946524208144t^55 + 2467095245250t^56 + 3109981870291t^57 + 3899707778226t^58 + 4864758338084t^59 + 6038049238675t^60 + 7457378700401t^61 + 9165927715226t^62 + 11212723264911t^63 + 13653141566979t^64 + 16549347183387t^65 + 19970759966163t^66 + 23994424008053t^67 + 28705388495679t^68 + 34196950655128t^69 + 40570891843897t^70 + 47937531085658t^71 + 56415752168625t^72 + 66132800675574t^73 + 77224036793196t^74 + 89832410691882t^75 + 104107880721344t^76 + 120206510443320t^77 + 138289504277080t^78 + 158521885428959t^79 + 181071120920863t^80 + 206105363625597t^81 + 233791665949818t^82 + 264293800024765t^83 + 297770093432862t^84 + 334370877999768t^85 + 374236019258930t^86 + 417492084225375t^87 + 464249676150170t^88 + 514600451190458t^89 + 568614408301291t^90 + 626336920289549t^91 + 687786160642371t^92 + 752950342462258t^93 + 821785485884455t^94 + 894213074068083t^95 + 970118373456853t^96 + 1049348716366855t^97 + 1131712577949459t^98 + 1216978678300190t^99 + 1304875993404447t^100 + 1395093834298654t^101 + 1487282925178084t^102 + 1581056564322066t^103 + 1675992841680187t^104 + 1771636919407880t^105 + 1867504387728908t^106 + 1963084625347838t^107 + 2057845212109979t^108 + 2151236247650709t^109 + 2242695657576844t^110 + 2331654270014146t^111 + 2417541776323760t^112 + 2499792295577520t^113 + 2577850688959356t^114 + 2651178288955232t^115 + 2719259223507973t^116 + 2781605956195677t^117 + 2837765257346956t^118 + 2887323196198862t^119 + 2929910405074852t^120 + 2965206186731099t^121 + 2992942753356401t^122 + 3012908161933130t^123 + 3024949270785865t^124 + 3028973288002032t^125 + 3024949270785865t^126 + 3012908161933130t^127 + 2992942753356401t^128 + 2965206186731099t^129 + 2929910405074852t^130 + 2887323196198862t^131 + 2837765257346956t^132 + 2781605956195677t^133 + 2719259223507973t^134 + 2651178288955232t^135 + 2577850688959356t^136 + 2499792295577520t^137 + 2417541776323760t^138 + 2331654270014146t^139 + 2242695657576844t^140 + 2151236247650709t^141 + 2057845212109979t^142 + 1963084625347838t^143 + 1867504387728908t^144 + 1771636919407880t^145 + 1675992841680187t^146 + 1581056564322066t^147 + 1487282925178084t^148 + 1395093834298654t^149 + 1304875993404447t^150 + 1216978678300190t^151 + 1131712577949459t^152 + 1049348716366855t^153 + 970118373456853t^154 + 894213074068083t^155 + 821785485884455t^156 + 752950342462258t^157 + 687786160642371t^158 + 626336920289549t^159 + 568614408301291t^160 + 514600451190458t^161 + 464249676150170t^162 + 417492084225375t^163 + 374236019258930t^164 + 334370877999768t^165 + 297770093432862t^166 + 264293800024765t^167 + 233791665949818t^168 + 206105363625597t^169 + 181071120920863t^170 + 158521885428959t^171 + 138289504277080t^172 + 120206510443320t^173 + 104107880721344t^174 + 89832410691882t^175 + 77224036793196t^176 + 66132800675574t^177 + 56415752168625t^178 + 47937531085658t^179 + 40570891843897t^180 + 34196950655128t^181 + 28705388495679t^182 + 23994424008053t^183 + 19970759966163t^184 + 16549347183387t^185 + 13653141566979t^186 + 11212723264911t^187 + 9165927715226t^188 + 7457378700401t^189 + 6038049238675t^190 + 4864758338084t^191 + 3899707778226t^192 + 3109981870291t^193 + 2467095245250t^194 + 1946524208144t^195 + 1527289937061t^196 + 1191539827621t^197 + 924180944791t^198 + 712520954002t^199 + 545958588510t^200 + 415686796764t^201 + 314440780906t^202 + 236260806268t^203 + 176294077526t^204 + 130611273929t^205 + 96055848819t^206 + 70106566677t^207 + 50766544654t^208 + 36463444967t^209 + 25970411969t^210 + 18335849747t^211 + 12828922109t^212 + 8891714037t^213 + 6102914802t^214 + 4146285473t^215 + 2787305828t^216 + 1853082547t^217 + 1217881983t^218 + 790779399t^219 + 507041603t^220 + 320813495t^221 + 200201862t^222 + 123110049t^223 + 74560924t^224 + 44423184t^225 + 26025211t^226 + 14968148t^227 + 8449357t^228 + 4670438t^229 + 2528528t^230 + 1336028t^231 + 689947t^232 + 346121t^233 + 169421t^234 + 80010t^235 + 36859t^236 + 16199t^237 + 6991t^238 + 2808t^239 + 1140t^240 + 410t^241 + 161t^242 + 50t^243 + 22t^244 + 5t^245 + 3t^246 + t^250) / (1 - t^2)(1 - t^3)(1 - t^4) (1 - t^5)(1 - t^6)(1 - t^7)(1 - t^8)(1 - t^9)(1 - t^10)(1 - t^11) (1 - t^12)(1 - t^13)(1 - t^14)(1 - t^15)(1 - t^16)(1 - t^17) (1 - t^18)(1 - t^19)(1 - t^20)(1 - t^21)(1 - t^22)(1 - t^23) CROSSREFS For these Poincaré series for d = 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 20, 24 see A097852, A293933, A097851, A293934, A293935, A293936, A293937, A293938, A293939, A293940, A293941, A293942, A293943 respectively. Sequence in context: A153121 A280926 A070153 * A171619 A153411 A081630 Adjacent sequences:  A293940 A293941 A293942 * A293944 A293945 A293946 KEYWORD nonn AUTHOR N. J. A. Sloane, Oct 20 2017 EXTENSIONS More terms from R. J. Mathar, Oct 26 2017 STATUS approved

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Last modified September 27 17:05 EDT 2021. Contains 347693 sequences. (Running on oeis4.)