A293939 Poincaré series for invariant polynomial functions on the space of binary forms of degree 14.

1, 0, 1, 0, 3, 0, 10, 4, 31, 27, 97, 110, 291, 375, 802, 1111, 2077, 2930, 5034, 7120, 11463, 16133, 24737, 34435, 50866, 69904, 100123, 135828, 189639, 253889, 346959, 458657, 615228, 803647, 1060615, 1369871, 1782235, 2277690, 2925659, 3702394, 4701294, 5894945, 7408011

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..42.

Andries Brouwer, Poincaré Series (See n=14)

Example

The Poincaré series is (1 + t^4 - t^5 + 5t^6 + 3t^7 + 18t^8 + 21t^9 + 56t^10 + 72t^11 + 155t^12 + 209t^13 + 375t^14 + 523t^15 + 836t^16 + 1131t^17 + 1695t^18 + 2234t^19 + 3132t^20 + 4029t^21 + 5371t^22 + 6691t^23 + 8566t^24 + 10348t^25 + 12736t^26 + 14971t^27 + 17789t^28 + 20306t^29 + 23400t^30 + 25973t^31 + 29023t^32 + 31385t^33 + 34068t^34 + 35858t^35 + 37893t^36 + 38831t^37 + 39932t^38 + 39890t^39 + 39932t^40 + 38831t^41 + 37893t^42 + 35858t^43 + 34068t^44 + 31385t^45 + 29023t^46 + 25973t^47 + 23400t^48 + 20306t^49 + 17789t^50 + 14971t^51 + 12736t^52 + 10348t^53 + 8566t^54 + 6691t^55 + 5371t^56 + 4029t^57 + 3132t^58 + 2234t^59 + 1695t^60 + 1131t^61 + 836t^62 + 523t^63 + 375t^64 + 209t^65 + 155t^66 + 72t^67 + 56t^68 + 21t^69 + 18t^70 + 3t^71 + 5t^72 - t^73 + t^74 + t^78) / (1 - t^2)(1 - t^4)(1 - t^5)(1 - t^6)^2(1 - t^7)(1 - t^8)(1 - t^9)(1 - t^10)(1 - t^11)(1 - t^12)(1 - t^13)

Maple

nmax := 120 :
(1 + t^4 - t^5 + 5*t^6 + 3*t^7 + 18*t^8 + 21*t^9 + 56*t^10 + 72*t^11 + 155*t^12 + 209*t^13 + 375*t^14 + 523*t^15 + 836*t^16 + 1131*t^17 + 1695*t^18 + 2234*t^19 + 3132*t^20 + 4029*t^21 + 5371*t^22 + 6691*t^23 + 8566*t^24 + 10348*t^25 + 12736*t^26 + 14971*t^27 + 17789*t^28 + 20306*t^29 + 23400*t^30 + 25973*t^31 + 29023*t^32 + 31385*t^33 + 34068*t^34 + 35858*t^35 + 37893*t^36 + 38831*t^37 + 39932*t^38 + 39890*t^39 + 39932*t^40 + 38831*t^41 + 37893*t^42 + 35858*t^43 + 34068*t^44 + 31385*t^45 + 29023*t^46 + 25973*t^47 + 23400*t^48 + 20306*t^49 + 17789*t^50 + 14971*t^51 + 12736*t^52 + 10348*t^53 + 8566*t^54 + 6691*t^55 + 5371*t^56 + 4029*t^57 + 3132*t^58 + 2234*t^59 + 1695*t^60 + 1131*t^61 + 836*t^62 + 523*t^63 + 375*t^64 + 209*t^65 + 155*t^66 + 72*t^67 + 56*t^68 + 21*t^69 + 18*t^70 + 3*t^71 + 5*t^72 - t^73 + t^74 + t^78) / (1 - t^2)/(1 - t^4)/(1 - t^5)/(1 - t^6)^2/(1 - t^7)/(1 - t^8)/(1 - t^9)/(1 - t^10)/(1 - t^11)/(1 - t^12)/(1 - t^13) ;
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: A094052 A161678 A232267 * A342926 A119957 A028852

Adjacent sequences: A293936 A293937 A293938 * A293940 A293941 A293942

Keyword

nonn

Author

N. J. A. Sloane, Oct 20 2017

Status

approved