A293943 Poincaré series for invariant polynomial functions on the space of binary forms of degree 24.

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

Offset

0,5

Comments

Many of these Poincaré series has every other term zero, in which case these zeros have been omitted.

Links

Table of n, a(n) for n=0..35.

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