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A001240
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G.f.: 1/((1-2x)(1-3x)(1-6x)).
(Formerly M4798 N2049)
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3
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1, 11, 85, 575, 3661, 22631, 137845, 833375, 5019421, 30174551, 181222405, 1087861775, 6528756781, 39177307271, 235078159765, 1410511939775, 8463200647741, 50779591044791, 304678708005925
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Differences of reciprocals of unity.
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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).
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..100
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
Index entries for sequences related to linear recurrences with constant coefficients
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FORMULA
| a(n) = 11a(n-1)-36a(n-2)+36a(n-3). - John W. Layman (layman(AT)math.vt.edu).
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 (vladeta(AT)eunet.rs), Aug 09 2002
a(n)=sum{0<=i,j,k,<=n, i+j+k=n, 2^i*3^j*6^k}. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 25 2007
a(n) = 2^n+3^(n+1)*(2^n-1). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 25 2007
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MAPLE
| A001240:=-1/((6*z-1)*(3*z-1)*(2*z-1)); [Conjectured (correctly) by S. Plouffe in his 1992 dissertation.]
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MATHEMATICA
| CoefficientList[Series[1/((1-2x)(1-3x)(1-6x)), {x, 0, 25}], x] (* or *) LinearRecurrence[{11, -36, 36}, {1, 11, 85}, 25] (* From Harvey P. Dale, May 15 2011 *)
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CROSSREFS
| Right-hand column 2 in triangle A008969.
a(n)=A112492(n+1, 3).
Sequence in context: A191003 A012478 A026783 * A129180 A082365 A012794
Adjacent sequences: A001237 A001238 A001239 * A001241 A001242 A001243
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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