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A293938
Poincaré series for invariant polynomial functions on the space of binary forms of degree 13.
13
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
OFFSET
0,3
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=13)
EXAMPLE
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)
MAPLE
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](%) ;
seq( %[1+2*i], i=0..nmax/2-1) ; # 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: A256303 A156438 A282134 * A254042 A368014 A009378
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Oct 20 2017
STATUS
approved