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A285201
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Stage at which Ken Knowlton's elevator (version 1) reaches floor n for the first time.
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6
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1, 2, 5, 14, 45, 174, 825, 4738, 32137, 251338, 2224157, 21952358, 238962581, 2843085270, 36696680241, 510647009850, 7619901954001, 121367981060434, 2055085325869813, 36861997532438654, 698193329457246653, 13924819967953406654, 291683979376372766697, 6402385486361598687666, 146948520147021794869977
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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a(n) = 2 - n + 2 * Sum_{k=0..n-2} Sum_{j=0..k} k!/j!.
For n >= 2, a(n) = 1+n+2*Sum_{k=2..n} C(n,k)*(k-1)! = 1+n+2*n!*Sum_{k=2..n} 1/(k*(n-k)!). - N. J. A. Sloane, May 03 2017
E.g.f.: exp(x)*(1-x-2*log(1-x)). Omitting the factor exp(x), this gives (essentially) the e.g.f. for A098558 (or A052849). - N. J. A. Sloane, May 03 2017
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MAPLE
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a:= proc(n) option remember; `if`(n<3, n, ((n-1)^2*a(n-1)
-(n-2)*(2*n-3)*a(n-2)+(n-1)*(n-3)*a(n-3))/(n-2))
end:
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MATHEMATICA
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a[n_] := 2 - n + 2 Sum[k!/j!, {k, 0, n-2}, {j, 0, k}];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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R. L. Graham, May 02 2017
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STATUS
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approved
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