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Search: id:A001240
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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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+0
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; listen)
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OFFSET
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1,2
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COMMENT
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Differences of reciprocals of unity.
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REFERENCES
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F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 228.
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LINKS
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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.
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FORMULA
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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.yu), 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
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A001240:=-1/((6*z-1)*(3*z-1)*(2*z-1)); [Conjectured (correctly) by S. Plouffe in his 1992 dissertation.]
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CROSSREFS
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Right-hand column 2 in triangle A008969.
a(n)=A112492(n+1, 3).
Adjacent sequences: A001237 A001238 A001239 this_sequence A001241 A001242 A001243
Sequence in context: A129077 A012478 A026783 this_sequence A129180 A082365 A012794
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KEYWORD
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nonn,easy,nice
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AUTHOR
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njas
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