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=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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Oct 20 2017
STATUS
approved