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A008667
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Generating function: 1/((1-x^2)(1-x^3)(1-x^4)(1-x^5)).
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0
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1, 0, 1, 1, 2, 2, 3, 3, 5, 5, 7, 7, 10, 10, 13, 14, 17, 18, 22, 23, 28, 29, 34, 36, 42, 44, 50, 53, 60, 63, 71, 74, 83, 87, 96, 101, 111, 116, 127, 133, 145, 151, 164, 171, 185, 193, 207, 216, 232, 241, 258, 268, 286, 297, 316, 328, 348, 361, 382, 396, 419, 433, 457
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Molien series for 4-dimensional complex reflection group of order 2^7 .3^5 .5.
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REFERENCES
| L. Smith, Polynomial Invariants of Finite Groups, Peters, 1995, p. 199 (No. 32).
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LINKS
| INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 241
Index entries for Molien series
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FORMULA
| Euler transform of length 5 sequence [ 0, 1, 1, 1, 1]. - Michael Somos Sep 23 2006
a(-14-n)=-a(n). - Michael Somos Sep 23 2006
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EXAMPLE
| a(4)=2 because f''''(x)/4!=2 at x=0 for f=1/((1-x^2)(1-x^3)(1-x^4)(1-x^5))
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MAPLE
| 1/(1-x^12)/(1-x^18)/(1-x^24)/(1-x^30)
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MATHEMATICA
| <<DiscreteMath`; SeriesTerm[1/((1-x^2)(1-x^3)(1-x^4)(1-x^5)), {x, 0, #}]&/@Range[0, 100] or a[k_]=SeriesTerm[1/((1-x^2)(1-x^3)(1-x^4)(1-x^5)), {x, 0, k}] - Peter Pein (petsie(AT)dordos.net), Sep 09 2006
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PROG
| (PARI) {a(n)=if(n<-13, -a(-14-n), polcoeff( prod(k=2, 5, 1/(1-x^k), 1+x*O(x^n)), n))} /* Michael Somos Oct 14 2006 */
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CROSSREFS
| Cf. A005044.
Sequence in context: A064986 A029019 A040039 * A177716 A109763 A119620
Adjacent sequences: A008664 A008665 A008666 * A008668 A008669 A008670
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Peter Pein (petsie(AT)dordos.net), Sep 09 2006
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