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A293938
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Poincaré series for invariant polynomial functions on the space of binary forms of degree 13.
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13
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1, 0, 2, 0, 22, 33, 181, 375, 1120, 2342, 5467, 10668, 21660, 39562, 72816, 125484, 215161, 352424, 572086, 897867, 1394315, 2110350, 3159826, 4635480, 6731131, 9612072, 13595657, 18964299, 26221103, 35828058, 48562922, 65155439, 86777107, 114549589, 150198041, 195400674, 252651242
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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 + 19t^8 + 31t^10 + 157t^12 + 321t^14 + 885t^16 + 1756t^18 + 3794t^20 + 6856t^22 + 12788t^24 + 21324t^26 + 35633t^28 + 55326t^30 + 85174t^32 + 124064t^34 + 178645t^36 + 246238t^38 + 334814t^40 + 439321t^42 + 568305t^44 + 712862t^46 + 881834t^48 + 1061455t^50 + 1259989t^52 + 1459221t^54 + 1666984t^56 + 1860904t^58 + 2049854t^60 + 2209072t^62 + 2349306t^64 + 2446352t^66 + 2514111t^68 + 2530530t^70 + 2514111t^72 + 2446352t^74 + 2349306t^76 + 2209072t^78 + 2049854t^80 + 1860904t^82 + 1666984t^84 + 1459221t^86 + 1259989t^88 + 1061455t^90 + 881834t^92 + 712862t^94 + 568305t^96 + 439321t^98 + 334814t^100 + 246238t^102 + 178645t^104 + 124064t^106 + 85174t^108 + 55326t^110 + 35633t^112 + 21324t^114 + 12788t^116 + 6856t^118 + 3794t^120 + 1756t^122 + 885t^124 + 321t^126 + 157t^128 + 31t^130 + 19t^132 - t^134 + t^136 + t^140)/ (1 - t^4)(1 - t^6)(1 - t^8)(1 - t^10)(1 - t^12)(1 - t^14)(1 - t^16)(1 - t^18)(1 - t^20)(1 - t^22)(1 - t^24)
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MAPLE
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nmax := 120 :
(1 + t^4 - t^6 + 19*t^8 + 31*t^10 + 157*t^12 + 321*t^14 + 885*t^16 + 1756*t^18 + 3794*t^20 + 6856*t^22 + 12788*t^24 + 21324*t^26 + 35633*t^28 + 55326*t^30 + 85174*t^32 + 124064*t^34 + 178645*t^36 + 246238*t^38 + 334814*t^40 + 439321*t^42 + 568305*t^44 + 712862*t^46 + 881834*t^48 + 1061455*t^50 + 1259989*t^52 + 1459221*t^54 + 1666984*t^56 + 1860904*t^58 + 2049854*t^60 + 2209072*t^62 + 2349306*t^64 + 2446352*t^66 + 2514111*t^68 + 2530530*t^70 + 2514111*t^72 + 2446352*t^74 + 2349306*t^76 + 2209072*t^78 + 2049854*t^80 + 1860904*t^82 + 1666984*t^84 + 1459221*t^86 + 1259989*t^88 + 1061455*t^90 + 881834*t^92 + 712862*t^94 + 568305*t^96 + 439321*t^98 + 334814*t^100 + 246238*t^102 + 178645*t^104 + 124064*t^106 + 85174*t^108 + 55326*t^110 + 35633*t^112 + 21324*t^114 + 12788*t^116 + 6856*t^118 + 3794*t^120 + 1756*t^122 + 885*t^124 + 321*t^126 + 157*t^128 + 31*t^130 + 19*t^132 - t^134 + t^136 + t^140)/ (1 - t^4)/(1 - t^6)/(1 - t^8)/(1 - t^10)/(1 - t^12)/(1 - t^14)/(1 - t^16)/(1 - t^18)/(1 - t^20)/(1 - t^22)/(1 - t^24) ;
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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