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A053464
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a(n) = n*5^(n-1).
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14
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0, 1, 10, 75, 500, 3125, 18750, 109375, 625000, 3515625, 19531250, 107421875, 585937500, 3173828125, 17089843750, 91552734375, 488281250000, 2593994140625, 13732910156250, 72479248046875, 381469726562500
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OFFSET
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0,3
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COMMENTS
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With a different offset, number of n-permutations of 6 objects u, v, w, z, x, y with repetition allowed, containing exactly one u. - Zerinvary Lajos, Dec 28 2007
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REFERENCES
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A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} 5^(n-k)*binomial(n-k+1, k)*binomial(1, (k+1)/2)*(1-(-1)^k)/2. - Paul Barry, Oct 15 2004
a(n) = 10*a(n-1) - 25*a(n-2); n>1; a(0)=0, a(1)=1.
Fourth binomial transform of n (starting 0, 1, 10...) Convolution of powers of 5.
G.f.: x/(1-5*x)^2; E.g.f.: x*exp(5*x). - Paul Barry, Jul 22 2003
a(n) = - 25^n * a(-n) for all n in Z. - Michael Somos, Jun 26 2017
Sum_{n>=1} 1/a(n) = 5*log(5/4).
Sum_{n>=1} (-1)^(n+1)/a(n) = 5*log(6/5). (End)
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MATHEMATICA
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Table[n*5^(n-1), {n, 0, 20}] (* or *) LinearRecurrence[{10, -25}, {0, 1}, 30] (* Harvey P. Dale, Jul 22 2014 *)
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PROG
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(Sage) [lucas_number1(n, 10, 25) for n in range(0, 21)] # Zerinvary Lajos, Apr 26 2009
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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