A002041 Expansion of x/((1-x)(1-4x^2)(1-5x)). (Formerly M4216 N1759)

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

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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.

Index entries for linear recurrences with constant coefficients, signature (6,-1,-24,20).

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

Adjacent sequences: A002038 A002039 A002040 * A002042 A002043 A002044

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Extended by Vincenzo Librandi, Jun 12 2012

Status

approved