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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

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

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Last modified March 2 19:14 EST 2021. Contains 341756 sequences. (Running on oeis4.)