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A085538
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a(n) = n^5 - n^4.
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7
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0, 0, 16, 162, 768, 2500, 6480, 14406, 28672, 52488, 90000, 146410, 228096, 342732, 499408, 708750, 983040, 1336336, 1784592, 2345778, 3040000, 3889620, 4919376, 6156502, 7630848, 9375000, 11424400, 13817466, 16595712, 19803868, 23490000, 27705630, 32505856
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OFFSET
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0,3
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COMMENTS
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For n >= 1, a(n) is equal to the number of functions f:{1,2,3,4,5}->{1,2,...,n} such that for a fixed x in {1,2,3,4,5} and a fixed y in {1,2,...,n} we have f(x) <> y. - Aleksandar M. Janjic and Milan Janjic, Mar 13 2007
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LINKS
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FORMULA
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G.f.: 2*x^2*(x^3 + 18*x^2 + 33*x + 8)/(x-1)^6. - Colin Barker, Nov 06 2012
Sum_{n>=2} 1/a(n) = 4 - zeta(2) - zeta(3) - zeta(4). - Amiram Eldar, Jul 05 2020
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MAPLE
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a:=n->sum(sum(n^3, j=1..n), k=2..n): seq(a(n), n=0..31); # Zerinvary Lajos, May 09 2007
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MATHEMATICA
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Table[n^5 - n^4, {n, 0, 40}] (* or *) LinearRecurrence[{6, -15, 20, -15, 6, -1}, {0, 0, 16, 162, 768, 2500}, 40] (* Vladimir Joseph Stephan Orlovsky, Feb 20 2012 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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