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A053464
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a(n)=n*5^(n-1).
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10
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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 (zerinvarylajos(AT)yahoo.com), 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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Vincenzo Librandi, Table of n, a(n) for n = 0..500
F. Ellermann, Illustration of binomial transforms
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 756
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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
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MATHEMATICA
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Join[{a=0, b=1}, Table[c=10*b-25*a; a=b; b=c, {n, 60}]] (*From Vladimir Joseph Stephan Orlovsky, Jan 27 2011*)
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PROG
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a(n)=if(n<0, 0, n*5^(n-1)) /* Michael Somos Sep 12 2005 */
(Sage) [lucas_number1(n, 10, 25) for n in xrange(0, 21)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 26 2009]
(MAGMA) [n*(5^(n-1)): n in [0..30]]; // Vincenzo Librandi, Jun 09 2011
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CROSSREFS
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Cf. A002697 and A027471.
Cf. A001787.
Sequence in context: A073379 A022734 A027203 * A111998 A026935 A110127
Adjacent sequences: A053461 A053462 A053463 * A053465 A053466 A053467
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KEYWORD
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easy,nonn
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AUTHOR
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Barry E. Williams, Jan 13 2000
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EXTENSIONS
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More terms from James A. Sellers, Feb 02 2000
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STATUS
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approved
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