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A180119
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a(n) = (n+2)! * Sum_{k = 1..n} 1/((k+1)*(k+2)).
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9
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0, 1, 6, 36, 240, 1800, 15120, 141120, 1451520, 16329600, 199584000, 2634508800, 37362124800, 566658892800, 9153720576000, 156920924160000, 2845499424768000, 54420176498688000, 1094805903679488000, 23112569077678080000, 510909421717094400000, 11802007641664880640000
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OFFSET
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0,3
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COMMENTS
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In general, a sequence of the form (n+x+2)! * Sum_{k = 1..n} (k+x)!/(k+x+2)! will have a closed form of (n+x+2)!*n/((x+2)*(n+2+x)).
Sum of the entries in all cycles of all permutations of [n]. - Alois P. Heinz, Apr 19 2017
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LINKS
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FORMULA
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a(n) = n*(n+1)!/2. [Simplified by M. F. Hasler, Apr 10 2018]
a(n) = (n+1)! * Sum_{k = 2..n} (1/(k^2+k)), with offset 1. - Gary Detlefs, Sep 15 2011
a(n) = Sum_{k = 0..n} (-1)^(n-k)*binomial(n,k)*k^(n+1) = (1/(2*x + 1))*Sum_{k = 0..n} (-1)^(n-k)*binomial(n,k)*(x*n + k)^(n+1), for arbitrary x != -1/2. - Peter Bala, Feb 19 2017
E.g.f.: x/(1-x)^3. (End)
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MAPLE
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a:= n-> n*(n+2)!/(2*(n+2)): seq(a(n), n=0..20);
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MATHEMATICA
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PROG
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(PARI) a(n) = (n+2)! * sum(k=1, n, 1/((k+1)*(k+2))); \\ Michel Marcus, Jan 10 2015
(Magma) [n*Factorial(n+2)/(2*(n+2)): n in [0..25]]; // Vincenzo Librandi, Feb 20 2017
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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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