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A293941 Poincaré series for invariant polynomial functions on the space of binary forms of degree 16. 13
1, 0, 1, 1, 3, 4, 13, 18, 47, 84, 177, 320, 639, 1120, 2077, 3581, 6235, 10395, 17344, 27940, 44848, 70180, 108921, 165817, 250256, 371558, 546960, 794363, 1143783, 1628190, 2299144, 3214042, 4459495, 6133164, 8375820, 11349269, 15278595, 20423345, 27136816, 35827488, 47037493, 61397294, 79726515, 102977471, 132370606, 169322488, 215620140, 273339320, 345063648, 433787088, 543198659, 677563207, 842079818, 1042751237, 1286826668, 1582652314, 1940231900, 2371051392, 2888771603, 3509044867, 4250358055, 5133832789, 6184270777, 7429930460 (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..63.

Andries Brouwer, Poincaré Series (See n=16)

EXAMPLE

The Poincaré series is (1 + t^4 + 2t^5 + 8t^6 + 11t^7 + 28t^8 + 51t^9 + 102t^10 + 177t^11 + 340t^12 + 561t^13 + 980t^14 + 1586t^15 + 2565t^16 + 3955t^17 + 6095t^18 + 8991t^19 + 13206t^20 + 18815t^21 + 26498t^22 + 36437t^23 + 49596t^24 + 66028t^25 + 87003t^26 + 112578t^27 + 144034t^28 + 181363t^29 + 226014t^30 + 277437t^31 + 337179t^32 + 404317t^33 + 479951t^34 + 562691t^35 + 653453t^36 + 749807t^37 + 852481t^38 + 958443t^39 + 1067723t^40 + 1176799t^41 + 1285637t^42 + 1389850t^43 + 1489589t^44 + 1580460t^45 + 1662409t^46 + 1731403t^47 + 1788102t^48 + 1828489t^49 + 1854175t^50 + 1862064t^51 + 1854175t^52 + 1828489t^53 + 1788102t^54 + 1731403t^55 + 1662409t^56 + 1580460t^57 + 1489589t^58 + 1389850t^59 + 1285637t^60 + 1176799t^61 + 1067723t^62 + 958443t^63 + 852481t^64 + 749807t^65 + 653453t^66 + 562691t^67 + 479951t^68 + 404317t^69 + 337179t^70 + 277437t^71 + 226014t^72 + 181363t^73 + 144034t^74 + 112578t^75 + 87003t^76 + 66028t^77 + 49596t^78 + 36437t^79 + 26498t^80 + 18815t^81 + 13206t^82 + 8991t^83 + 6095t^84 + 3955t^85 + 2565t^86 + 1586t^87 + 980t^88 + 561t^89 + 340t^90 + 177t^91 + 102t^92 + 51t^93 + 28t^94 + 11t^95 + 8t^96 + 2t^97 + t^98 + t^102) / (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)

MAPLE

nmax := 120 :

(1 + t^4 + 2*t^5 + 8*t^6 + 11*t^7 + 28*t^8 + 51*t^9 + 102*t^10 + 177*t^11 + 340*t^12 + 561*t^13 + 980*t^14 + 1586*t^15 + 2565*t^16 + 3955*t^17 + 6095*t^18 + 8991*t^19 + 13206*t^20 + 18815*t^21 + 26498*t^22 + 36437*t^23 + 49596*t^24 + 66028*t^25 + 87003*t^26 + 112578*t^27 + 144034*t^28 + 181363*t^29 + 226014*t^30 + 277437*t^31 + 337179*t^32 + 404317*t^33 + 479951*t^34 + 562691*t^35 + 653453*t^36 + 749807*t^37 + 852481*t^38 + 958443*t^39 + 1067723*t^40 + 1176799*t^41 + 1285637*t^42 + 1389850*t^43 + 1489589*t^44 + 1580460*t^45 + 1662409*t^46 + 1731403*t^47 + 1788102*t^48 + 1828489*t^49 + 1854175*t^50 + 1862064*t^51 + 1854175*t^52 + 1828489*t^53 + 1788102*t^54 + 1731403*t^55 + 1662409*t^56 + 1580460*t^57 + 1489589*t^58 + 1389850*t^59 + 1285637*t^60 + 1176799*t^61 + 1067723*t^62 + 958443*t^63 + 852481*t^64 + 749807*t^65 + 653453*t^66 + 562691*t^67 + 479951*t^68 + 404317*t^69 + 337179*t^70 + 277437*t^71 + 226014*t^72 + 181363*t^73 + 144034*t^74 + 112578*t^75 + 87003*t^76 + 66028*t^77 + 49596*t^78 + 36437*t^79 + 26498*t^80 + 18815*t^81 + 13206*t^82 + 8991*t^83 + 6095*t^84 + 3955*t^85 + 2565*t^86 + 1586*t^87 + 980*t^88 + 561*t^89 + 340*t^90 + 177*t^91 + 102*t^92 + 51*t^93 + 28*t^94 + 11*t^95 + 8*t^96 + 2*t^97 + t^98 + t^102) / (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) ;

taylor(%, t=0, nmax) ;

gfun[seriestolist](%) ; # R. J. Mathar, Oct 26 2017

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: A291250 A205901 A302392 * A182691 A026700 A187775

Adjacent sequences:  A293938 A293939 A293940 * A293942 A293943 A293944

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Oct 20 2017

STATUS

approved

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Last modified September 17 01:53 EDT 2021. Contains 347478 sequences. (Running on oeis4.)