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A293934
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Poincaré series for invariant polynomial functions on the space of binary forms of degree 9.
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13
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1, 0, 2, 0, 8, 5, 28, 27, 84, 99, 217, 273, 506, 647, 1066, 1367, 2082, 2649, 3811, 4796, 6612, 8228, 10960, 13483, 17487, 21274, 26979, 32490, 40443, 48242, 59107, 69885, 84470, 99074, 118330, 137762, 162842, 188287, 220516, 253377, 294316, 336213, 387658, 440463, 504484
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OFFSET
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0,3
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COMMENTS
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Many of these Poincaré series has every other term zero, in which case these zeros have been omitted.
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LINKS
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EXAMPLE
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The Poincaré series is (1 + t^4 - t^6 + 5t^8 + 3t^10 + 18t^12 + 15t^14 + 44t^16 + 43t^18 + 82t^20 + 76t^22 + 122t^24 + 107t^26 + 147t^28 + 119t^30 + 147t^32 + 107t^34 + 122t^36 + 76t^38 + 82t^40 + 43t^42 + 44t^44 + 15t^46 + 18t^48 + 3t^50 + 5t^52 - t^54 + t^56 + t^60) / (1 - t^4)(1 - t^6)(1 - t^8)(1 - t^10)(1 - t^12)(1 - t^14)(1 - t^16)
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MAPLE
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nmax := 120 :
(1 + t^4 - t^6 + 5*t^8 + 3*t^10 + 18*t^12 + 15*t^14 + 44*t^16 + 43*t^18 + 82*t^20 + 76*t^22 + 122*t^24 + 107*t^26 + 147*t^28 + 119*t^30 + 147*t^32 + 107*t^34 + 122*t^36 + 76*t^38 + 82*t^40 + 43*t^42 + 44*t^44 + 15*t^46 + 18*t^48 + 3*t^50 + 5*t^52 - t^54 + t^56 + t^60) / (1 - t^4)/(1 - t^6)/(1 - t^8)/(1 - t^10)/(1 - t^12)/(1 - t^14)/(1 - t^16) ;
taylor(%, t=0, nmax) :
gfun[seriestolist](%) :
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CROSSREFS
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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.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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