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A265325
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Number of n-digit decimal numbers with leading zeros allowed where no digit appears exactly twice.
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3
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10, 90, 730, 5410, 37900, 264250, 1908910, 14322520, 110305720, 875799550, 7203731050, 60866700940, 527138423380, 4696469283970, 42797376850150, 397903278667600, 3783002076771760, 36604891556846470, 360117919584474850, 3603555076712108500
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OFFSET
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1,1
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LINKS
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FORMULA
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E.g.f.: Sum_{q=1..N} C(10,q)*(exp(z)-z^2/2-1)^q.
E.g.f.: (exp(z)-z^2/2)^10.
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EXAMPLE
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Computing the value for n=1 the ten one-digit numbers 0-9 all qualify.
Computing the value for n=2 of two-digit numbers 00-99 all qualify except those consisting of a double digit (00, 11, ..., 99).
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MAPLE
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STNE2 := (n, k)->n!*coeftayl((exp(z)-z^2/2-1)^k/k!, z=0, n);
a(N) := N -> add(combinat:-binomial(10, q)*STNE2(N, q)*q!, q = 1 .. N)
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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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STATUS
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approved
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