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A293937 Poincare 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Many of these Poincare series has every other term zero, in which case these zeros have been omitted.

LINKS

Table of n, a(n) for n=0..45.

Andries Brouwer, Poincaré Series (See n=12)

EXAMPLE

The Poincare 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 Poincare 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 A052407

Adjacent sequences:  A293934 A293935 A293936 * A293938 A293939 A293940

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Oct 20 2017

STATUS

approved

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Last modified November 19 08:44 EST 2019. Contains 329318 sequences. (Running on oeis4.)