A002625 Expansion of 1/((1-x)^3*(1-x^2)^2*(1-x^3)).
1, 3, 8, 17, 33, 58, 97, 153, 233, 342, 489, 681, 930, 1245, 1641, 2130, 2730, 3456, 4330, 5370, 6602, 8048, 9738, 11698, 13963, 16563, 19538, 22923, 26763, 31098, 35979, 41451, 47571, 54390, 61971, 70371, 79660, 89901, 101171, 113540, 127092, 141904, 158068, 175668, 194804, 215568
Offset: 0
References
- N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- E. Fix and J. L. Hodges, Jr., Significance probabilities of the Wilcoxon test, Annals Math. Stat., 26 (1955), 301-312.
- E. Fix and J. L. Hodges, Significance probabilities of the Wilcoxon test, Annals Math. Stat., 26 (1955), 301-312. [Annotated scanned copy]
- INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 205
- Gerzson Keri and Patric R. J. Östergård, The Number of Inequivalent (2R+3,7)R Optimal Covering Codes, Journal of Integer Sequences, Vol. 9 (2006), Article 06.4.7.
- Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
- Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
- Index entries for linear recurrences with constant coefficients, signature (3,-1,-4,2,2,2,-4,-1,3,-1).
Crossrefs
Partial sums of A097701.
Programs
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Maple
A002625:=1/(z**2+z+1)/(z+1)**2/(z-1)**6; [Simon Plouffe in his 1992 dissertation.]
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Mathematica
CoefficientList[Series[1/((1-x)^3*(1-x^2)^2*(1-x^3)),{x,0,50}],x] (* Vincenzo Librandi, Feb 25 2012 *) LinearRecurrence[{3,-1,-4,2,2,2,-4,-1,3,-1},{1,3,8,17,33,58,97,153,233,342},50] (* Harvey P. Dale, Sep 24 2022 *) -
PARI
Vec(1/(1-x)^3/(1-x^2)^2/(1-x^3)+O(x^99)) \\ Charles R Greathouse IV, Apr 30 2012
Formula
a(n) = floor((n+1)*(135*(-1)^n + 6*n^4 + 144*n^3 + 1256*n^2 + 4744*n + 6785)/8640+1/2). - Tani Akinari, Oct 07 2012
Comments