login
A293937
Poincaré series for invariant polynomial functions on the space of binary forms of degree 12.
13
1, 0, 1, 1, 3, 3, 8, 10, 20, 28, 52, 73, 127, 181, 291, 418, 639, 902, 1330, 1848, 2634, 3603, 4998, 6718, 9113, 12058, 16027, 20903, 27307, 35123, 45198, 57412, 72874, 91519, 114762, 142605, 176883, 217679, 267324, 326073, 396837, 480074, 579460, 695704, 833361, 993548
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
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: A245142 A123315 A237113 * A291857 A300672 A368726
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Oct 20 2017
STATUS
approved