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A293939 Poincare series for invariant polynomial functions on the space of binary forms of degree 14. 13
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 (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..42.

Andries Brouwer, Poincaré Series (See n=14)

EXAMPLE

The Poincare 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 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: A094052 A161678 A232267 * A119957 A028852 A319202

Adjacent sequences:  A293936 A293937 A293938 * A293940 A293941 A293942

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Oct 20 2017

STATUS

approved

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Last modified November 14 22:17 EST 2019. Contains 329134 sequences. (Running on oeis4.)