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A093461
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a(1)=1, a(n)=2[n^(n-1)-1]/(n-1) for n>=2.
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3
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1, 2, 8, 42, 312, 3110, 39216, 599186, 10761680, 222222222, 5187484920, 135092431034, 3883014187080, 122109965116022, 4170418003627232, 153722867280912930, 6082648984458358560, 257166065851611356702
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Proposition: n^(n-1) -1 == 0 (mod (n-1)^2). Hence a(n) == 0 mod (n-1).
a(n) is the common difference of the arithmetic progression in row n of A111568. Written in base n, a(n) has n-1 digits equal to 2 (for example, a(10)=222222222). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 08 2005
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FORMULA
| a(1) = 1, a(n) = 2*{n^(n-1) -1}}/{n-1} for n >1.
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MAPLE
| a:=proc(n) if n=1 then 1 else 2*(n^(n-1)-1)/(n-1) fi end: seq(a(n), n=1..20); (Deutsch)
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MATHEMATICA
| f[n_] := (2*n^(n-1) - 2)/(n-1); Table[f[i], {i, 2, 30}] (Propper)
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CROSSREFS
| Cf. A093460, A093462.
Cf. A111568.
Sequence in context: A078592 A052646 A002856 * A191994 A153524 A153552
Adjacent sequences: A093458 A093459 A093460 * A093462 A093463 A093464
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KEYWORD
| nonn
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Apr 05 2004
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EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu) and Ryan Propper (rpropper(AT)stanford.edu), Aug 08 2005
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