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A030297
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a(n) = n*(n + a(n-1)) with a(0)=0.
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17
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0, 1, 6, 27, 124, 645, 3906, 27391, 219192, 1972809, 19728190, 217010211, 2604122676, 33853594957, 473950329594, 7109254944135, 113748079106416, 1933717344809361, 34806912206568822, 661331331924807979
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OFFSET
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0,3
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COMMENTS
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LINKS
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FORMULA
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a(n) = sum_{k=0...n} (n! / k!) * k^2. - Ross La Haye, Sep 21 2004
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MAPLE
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f := proc(n) options remember; if n <= 1 then n elif n = 2 then 6 else -n*(n-2)*f(n-3)+(n-3)*n*f(n-2)+3*n*f(n-1)/(n-1); fi; end;
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MATHEMATICA
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RecurrenceTable[{a[0]==0, a[n]==n(n+a[n-1])}, a[n], {n, 20}] (* Harvey P. Dale, Oct 22 2011 *)
Round@Table[(2 E Gamma[n, 1] - 1) n, {n, 0, 20}] (* Round is equivalent to FullSimplify here, but is much faster - Vladimir Reshetnikov, Oct 07 2016 *)
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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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EXTENSIONS
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STATUS
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approved
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