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A002041
Expansion of x/((1-x)(1-4x^2)(1-5x)).
(Formerly M4216 N1759)
1
1, 6, 35, 180, 921, 4626, 23215, 116160, 581141, 2906046, 14531595, 72659340, 363302161, 1816516266, 9082603175, 45413037720, 227065275981, 1135326467286, 5676632685955, 28383163779300, 141915820294601, 709579102871106, 3547895519947935, 17739477605332080, 88697388049030021
OFFSET
1,2
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
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
G. B. M. Zerr et al., Problem 64, Amer. Math. Monthly, 3 (1896), 244-248.
FORMULA
a(n-2) = (1/252) {3*5^n - 4^[(n+2)/2] - 5*4^[(n+3)/2] + 21}. - Ralf Stephan, Aug 22 2004
MAPLE
A002041:=-1/(z-1)/(2*z+1)/(2*z-1)/(5*z-1); # conjectured by Simon Plouffe in his 1992 dissertation
MATHEMATICA
CoefficientList[Series[x/(1-x)/(1-4x^2)/(1-5x), {x, 1, 30}], x] (* Vincenzo Librandi, Jun 12 2012 *)
LinearRecurrence[{6, -1, -24, 20}, {0, 1, 6, 35}, 30] (* Harvey P. Dale, Aug 27 2022 *)
CROSSREFS
Sequence in context: A333800 A026997 A014337 * A103995 A137628 A254826
KEYWORD
nonn,easy
EXTENSIONS
Extended by Vincenzo Librandi, Jun 12 2012
STATUS
approved