A293936 Poincaré series for invariant polynomial functions on the space of binary forms of degree 11.

1, 0, 2, 0, 13, 13, 73, 110, 320, 529, 1160, 1893, 3569, 5633, 9600, 14636, 23246, 34233, 51618, 73716, 106678, 148325, 207652, 281963, 384141, 510882, 680155, 888201, 1159414, 1489689, 1911698, 2421067, 3060774, 3826640, 4774174, 5899837, 7274612, 8895981, 10853618, 13146996

Offset

0,3

Comments

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

Links

Table of n, a(n) for n=0..39.

Andries Brouwer, Poincaré Series (See n=11)

Example

The Poincaré series is (1 + t^4 - t^6 + 10t^8 + 11t^10 + 58t^12 + 85t^14 + 222t^16 + 336t^18 + 660t^20 + 951t^22 + 1589t^24 + 2154t^26 + 3188t^28 + 4080t^30 + 5510t^32 + 6633t^34 + 8310t^36 + 9443t^38 + 11059t^40 + 11894t^42 + 13094t^44 + 13319t^46 + 13852t^48 + 13319t^50 + 13094t^52 + 11894t^54 + 11059t^56 + 9443t^58 + 8310t^60 + 6633t^62 + 5510t^64 + 4080t^66 + 3188t^68 + 2154t^70 + 1589t^72 + 951t^74 + 660t^76 + 336t^78 + 222t^80 + 85t^82 + 58t^84 + 11t^86 + 10t^88 - t^90 + t^92 + t^96) / (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)

Maple

nmax := 120 :
(1 + t^4 - t^6 + 10*t^8 + 11*t^10 + 58*t^12 + 85*t^14 + 222*t^16 + 336*t^18 + 660*t^20 + 951*t^22 + 1589*t^24 + 2154*t^26 + 3188*t^28 + 4080*t^30 + 5510*t^32 + 6633*t^34 + 8310*t^36 + 9443*t^38 + 11059*t^40 + 11894*t^42 + 13094*t^44 + 13319*t^46 + 13852*t^48 + 13319*t^50 + 13094*t^52 + 11894*t^54 + 11059*t^56 + 9443*t^58 + 8310*t^60 + 6633*t^62 + 5510*t^64 + 4080*t^66 + 3188*t^68 + 2154*t^70 + 1589*t^72 + 951*t^74 + 660*t^76 + 336*t^78 + 222*t^80 + 85*t^82 + 58*t^84 + 11*t^86 + 10*t^88 - t^90 + t^92 + t^96) / (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) ;
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: A107700 A274107 A122688 * A110685 A225480 A286118

Adjacent sequences: A293933 A293934 A293935 * A293937 A293938 A293939

Keyword

nonn

Author

N. J. A. Sloane, Oct 20 2017

Status

approved