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A111177
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Number of base n numbers in which each digit appears at most once (all unnecessary 0's deleted).
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0
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4, 21, 130, 913, 7176, 62629, 602806, 6356865, 72994348, 907497301, 12152572554, 174476220241, 2674434002800, 43603430324133, 753581024080126, 13763517571878529, 264919276238885076, 5360264479811601685
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OFFSET
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2,1
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COMMENTS
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Finite expansions after the "decimal" point are allowed, but there must be a number before it (so we can have 0.1, but not .01).
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LINKS
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FORMULA
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a(n)=Sum(i=0, n-1) (i^2+i+1)(n-1)!/(n-1-i)!; n>1
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EXAMPLE
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a(2)=4 because in the binary system only the numbers 0; 1; 0.1; 10 can be written with each digit used at most once (all unnecessary 0's deleted).
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MATHEMATICA
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f[n_] := Sum[(i^2 + i + 1)(n - 1)!/(n - 1 - i)!, {i, 0, n - 1}]; Table[ f[n], {n, 2, 19}] (* Robert G. Wilson v *)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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Rafael Hofman (mathematics287(AT)yahoo.de), Oct 22 2005
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EXTENSIONS
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STATUS
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approved
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