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A213326
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a(n) = (n+2)^n - (n+1)^n.
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1
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0, 1, 7, 61, 671, 9031, 144495, 2685817, 56953279, 1357947691, 35979939623, 1049152023349, 33395827252815, 1152480295105231, 42864668012537311, 1709501546902968817, 72778339220927383295, 3294475298046105653971, 158016649702088758467159
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OFFSET
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0,3
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COMMENTS
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a(n) is the number of acyclic functions from subsets of size n-1 or less of {1,...,n+1} to {1,2,...,n+1}. - Dennis P. Walsh, Nov 06 2015
a(n) is the number of parking functions whose largest element is not n+1 and length is n+1. For example, a(2) = 7 because there are seven such parking functions, namely (1,1,1), (1,1,2), (1,2,1), (2,1,1), (1,2,2), (2,1,2), (2,2,1). - Ran Pan, Nov 15 2015
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LINKS
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FORMULA
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a(n) = Sum_{i=0..n-2} binomial(n,i)*((i+1)^(i-1)*(n-i-1)^(n-i-1))).
E.g.f.: LambertW(-x)*(LambertW(-x)+x)/((1+LambertW(-x))*x^2). - Alois P. Heinz, Aug 12 2017
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MAPLE
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MATHEMATICA
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Table[(n + 2)^n - (n + 1)^n, {n, 0, 20}] (* T. D. Noe, Mar 07 2013 *)
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PROG
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(Maxima) a(n):=sum(binomial(n, i)*((i+1)^(i-1)*(n-i-1)^(n-i-1)), i, 0, n-2);
(PARI) vector(40, n, n--; (n+2)^n-(n+1)^n) \\ Altug Alkan, Nov 11 2015
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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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