OFFSET
1,2
COMMENTS
Differences of reciprocals of unity.
REFERENCES
F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 228.
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
T. D. Noe, Table of n, a(n) for n = 1..100
Aung Phone Maw, Aung Kyaw, Recursive Harmonic Numbers and Binomial Coefficients, arXiv:1711.10716 [math.CO], 2017.
Mircea Merca, Some experiments with complete and elementary symmetric functions, Periodica Mathematica Hungarica, 69 (2014), 182-189.
Jerry Metzger and Thomas Richards, A Prisoner Problem Variation, Journal of Integer Sequences, Vol. 18 (2015), Article 15.2.7.
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 (11,-36,36).
FORMULA
a(n) = 11a(n-1) - 36a(n-2) + 36a(n-3). - John W. Layman
a(n) = (6^n - 2*3^n + 2^n)/2. Also -x^2/6*Beta(x, 4) = Sum_{n>=0} a(n)*(-x/6)^n. Thus x^2*Beta(x, 4) = x - 11/6*x^2 + 85/36*x^3 - 575/216*x^4 + 3661/1296*x^5 - ... . - Vladeta Jovovic, Aug 09 2002
a(n) = Sum_{0<=i,j,k,<=n, i+j+k=n} 2^i*3^j*6^k. - Hieronymus Fischer, Jun 25 2007
a(n) = 2^n + 3^(n+1)*(2^n-1). - Hieronymus Fischer, Jun 25 2007
a(n) = Sum_{k = 0..n-1} 2^(n-2-k) * (3^n - 3^k). - J. M. Bergot, Feb 05 2018
MAPLE
A001240:=-1/((6*z-1)*(3*z-1)*(2*z-1)); # conjectured (correctly) by Simon Plouffe in his 1992 dissertation
MATHEMATICA
CoefficientList[Series[1/((1-2x)(1-3x)(1-6x)), {x, 0, 25}], x] (* or *) LinearRecurrence[{11, -36, 36}, {1, 11, 85}, 25] (* Harvey P. Dale, May 15 2011 *)
PROG
(PARI) a(n)=(6^n-2*3^n+2^n)/2 \\ Charles R Greathouse IV, Feb 19 2017
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
STATUS
approved