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 A293934 Poincaré 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 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

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Last modified September 26 15:54 EDT 2023. Contains 365660 sequences. (Running on oeis4.)