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=12)
EXAMPLE
The Poincaré series is (1 + t^4 + t^5 + 3t^6 + 4t^7 + 7t^8 + 9t^9 + 17t^10 + 21t^11 + 36t^12 + 45t^13 + 65t^14 + 81t^15 + 110t^16 + 131t^17 + 168t^18 + 193t^19 + 232t^20 + 256t^21 + 293t^22 + 307t^23 + 336t^24 + 339t^25 + 351t^26 + 339t^27 + 336t^28 + 307t^29 + 293t^30 + 256t^31 + 232t^32 + 193t^33 + 168t^34 + 131t^35 + 110t^36 + 81t^37 + 65t^38 + 45t^39 + 36t^40 + 21t^41 + 17t^42 + 9t^43 + 7t^44 + 4t^45 + 3t^46 + t^47 + t^48 + t^52) / (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)
MAPLE
nmax := 120 :
(1 + t^4 + t^5 + 3*t^6 + 4*t^7 + 7*t^8 + 9*t^9 + 17*t^10 + 21*t^11 + 36*t^12 + 45*t^13 + 65*t^14 + 81*t^15 + 110*t^16 + 131*t^17 + 168*t^18 + 193*t^19 + 232*t^20 + 256*t^21 + 293*t^22 + 307*t^23 + 336*t^24 + 339*t^25 + 351*t^26 + 339*t^27 + 336*t^28 + 307*t^29 + 293*t^30 + 256*t^31 + 232*t^32 + 193*t^33 + 168*t^34 + 131*t^35 + 110*t^36 + 81*t^37 + 65*t^38 + 45*t^39 + 36*t^40 + 21*t^41 + 17*t^42 + 9*t^43 + 7*t^44 + 4*t^45 + 3*t^46 + t^47 + t^48 + t^52) / (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) ;
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