login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A293934 Poincare series for invariant polynomial functions on the space of binary forms of degree 9. 13
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Many of these Poincare 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 Poincare 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 Poincare 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: A321599 A020780 A243406 * A316133 A243443 A096609

Adjacent sequences:  A293931 A293932 A293933 * A293935 A293936 A293937

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Oct 20 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 20 10:09 EST 2019. Contains 329334 sequences. (Running on oeis4.)