A293935 - OEIS

A293935

Poincaré series for invariant polynomial functions on the space of binary forms of degree 10.

1, 0, 1, 0, 2, 0, 6, 0, 12, 5, 24, 13, 52, 33, 97, 80, 177, 160, 319, 301, 540, 547, 887, 926, 1429, 1512, 2219, 2402, 3367, 3681, 5015, 5502, 7294, 8064, 10419, 11550, 14664, 16253, 20287, 22531, 27682, 30738, 37319, 41378, 49671, 55060, 65390, 72391, 85250

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OFFSET

0,5

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..48.

Andries Brouwer, Poincaré Series (See n=10)

EXAMPLE

The Poincaré series is (1 - t^5 + 2t^6 - t^7 + 4t^8 + 4t^9 + 8t^10 + 6t^11 + 16t^12 + 9t^13 + 17t^14 + 15t^15 + 19t^16 + 12t^17 + 23t^18 + 12t^19 + 19t^20 + 15t^21 + 17t^22 + 9t^23 + 16t^24 + 6t^25 + 8t^26 + 4t^27 + 4t^28 - t^29 + 2t^30 - t^31 + t^36) / (1 - t^2)(1 - t^4)(1 - t^5)(1 - t^6)^2(1 - t^7)(1 - t^8)(1 - t^9)

MAPLE

nmax := 120 :

(1 - t^5 + 2*t^6 - t^7 + 4*t^8 + 4*t^9 + 8*t^10 + 6*t^11 + 16*t^12 + 9*t^13 + 17*t^14 + 15*t^15 + 19*t^16 + 12*t^17 + 23*t^18 + 12*t^19 + 19*t^20 + 15*t^21 + 17*t^22 + 9*t^23 + 16*t^24 + 6*t^25 + 8*t^26 + 4*t^27 + 4*t^28 - t^29 + 2*t^30 - t^31 + t^36) / (1 - t^2)/(1 - t^4)/(1 - t^5)/(1 - t^6)^2/(1 - t^7)/(1 - t^8)/(1 - t^9) ;

taylor(%, t=0, nmax) ;

gfun[seriestolist](%) ;

seq( %[1+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: A328337 A285782 A285538 * A285479 A327369 A296620

Adjacent sequences: A293932 A293933 A293934 * A293936 A293937 A293938

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Oct 20 2017

STATUS

approved