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 A008668 Molien series for 4-dimensional reflection group [3,3,5] of order 14400. 1
 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 4, 5, 6, 6, 7, 7, 8, 9, 10, 10, 11, 12, 13, 14, 15, 15, 18, 19, 20, 21, 22, 23, 26, 27, 28, 29, 32, 33, 36, 37, 38, 41, 44, 45, 48, 49, 52, 55, 58, 59, 62, 65, 68, 71, 74, 75, 81, 84, 87, 90, 93, 96, 102, 105, 108, 111, 117, 120, 126, 129, 132, 138 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 COMMENTS The relevant generating function is 1/((1-z^2)*(1-z^12)*(1-z^20)*(1-z^30)) and is reduced with x=z^2 below to indicate that the intermediate zeros are not listed. Number of partitions into parts 1, 6, 10, and 15. - Joerg Arndt, Apr 29 2014 REFERENCES H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups, Ergebnisse der Mathematik und Ihrer Grenzgebiete, New Series, no. 14. Springer Verlag, 1957, Table 10. L. Smith, Polynomial Invariants of Finite Groups, Peters, 1995, p. 199 (No. 30). LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Roberto De Maria Nunes Mendes, Symmetries of spherical harmonics, Transactions of the American Mathematical Society 204 (1975): 161-178. See subgroup 68. INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 240 Index entries for Molien series Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 1, -1, 0, 0, 1, -1, 0, 0, 0, 1, -2, 1, 0, 0, 0, -1, 1, 0, 0, -1, 1, 0, 0, 0, 0, 1, -1). FORMULA G.f.: 1/((1-x)*(1-x^6)*(1-x^10)*(1-x^15)). - M. F. Hasler, Mar 26 2012 a(n) ~ 1/5400*n^3. - Ralf Stephan, Apr 29 2014 MAPLE seq(coeff(series(1/((1-x)*(1-x^6)*(1-x^10)*(1-x^15)), x, n+1), x, n), n = 0 .. 80); # G. C. Greubel, Sep 08 2019 MATHEMATICA CoefficientList[Series[1/((1-x)*(1-x^6)*(1-x^10)*(1-x^15)), {x, 0, 80}], x] (* G. C. Greubel, Sep 08 2019 *) PROG (PARI) A008668_list = n -> Vec(1/((1-x)*(1-x^6)*(1-x^10)*(1-x^15)) +O(x^n)) \\ M. F. Hasler, Mar 26 2012 (Magma) R:=PowerSeriesRing(Integers(), 80); Coefficients(R!( 1/((1-x)*(1-x^6)*(1-x^10)*(1-x^15)) )); // G. C. Greubel, Sep 08 2019 (Sage) def A008668_list(prec): P. = PowerSeriesRing(ZZ, prec) return P(1/((1-x)*(1-x^6)*(1-x^10)*(1-x^15))).list() A008668_list(80) # G. C. Greubel, Sep 08 2019 CROSSREFS Sequence in context: A056970 A212218 A321162 * A225643 A116563 A076695 Adjacent sequences: A008665 A008666 A008667 * A008669 A008670 A008671 KEYWORD nonn AUTHOR N. J. A. Sloane EXTENSIONS Terms a(61) onward added by G. C. Greubel, Sep 08 2019 STATUS approved

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Last modified November 30 19:18 EST 2023. Contains 367462 sequences. (Running on oeis4.)