A293934 Poincaré series for invariant polynomial functions on the space of binary forms of degree 9.

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

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..44.

Andries Brouwer, Poincaré Series (See n=9)

Example

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)

Maple

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](%) :
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: A020780 A334071 A243406 * A356651 A316133 A359451

Adjacent sequences: A293931 A293932 A293933 * A293935 A293936 A293937

Keyword

nonn

Author

N. J. A. Sloane, Oct 20 2017

Status

approved