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A006550
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n+8*C(n,2)+30*C(n,3)+62*C(n,4)+75*C(n,5)+30*C(n,6).
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5
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0, 1, 10, 57, 234, 770, 2136, 5180, 11292, 22599, 42190, 74371, 124950, 201552, 313964, 474510, 698456, 1004445, 1414962, 1956829, 2661730, 3566766, 4715040, 6156272, 7947444, 10153475, 12847926, 16113735, 20043982, 24742684, 30325620
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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REFERENCES
| 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.
L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 254, gives this as number of ways to color faces of a cube using at most n colors, but the formula is incorrect - see A047780.
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LINKS
| 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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MAPLE
| A006550:=(-1-3*z-8*z**2-10*z**3-14*z**4+6*z**5)/(z-1)**7; [Conjectured by S. Plouffe in his 1992 dissertation.]
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MATHEMATICA
| Table[n+8Binomial[n, 2]+30Binomial[n, 3]+62Binomial[n, 4]+75Binomial[n, 5]+ 30Binomial[n, 6], {n, 0, 40}] (* or *) LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 1, 10, 57, 234, 770, 2136}, 40] (* From Harvey P. Dale, Apr 24 2011 *)
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CROSSREFS
| Sequence in context: A034195 A067250 A061005 * A047780 A055251 A038733
Adjacent sequences: A006547 A006548 A006549 * A006551 A006552 A006553
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Jud McCranie (JudMcCranie(AT)ugaalum.uga.edu) found this error and gave the correct version of this sequence (A047780).
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