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A182430
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a(n) = n! - A003149(n-1).
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0
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1, 0, 0, 1, 8, 56, 408, 3228, 28032, 267264, 2787840, 31662720, 389560320, 5166650880, 73528680960, 1118124000000, 18098712576000, 310759981056000, 5642339254272000, 108022399414272000, 2175029897822208000
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OFFSET
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0,5
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COMMENTS
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a(n) is the number of fixed points over all permutations of {1,2,...,n} that are not strong fixed points. Definition by Emeric Deutsch in A003149: a permutation p of {1,2,...,n} is said to have j as a strong fixed point (splitter) if p(k)<j for k<j and p(k)>j for k>j.
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LINKS
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FORMULA
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O.g.f.: (1-x-I(x))/(1-I(x))^2 where I(x) is the o.g.f. for A003319.
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EXAMPLE
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a(4)=8 because we have: 1_43'2, 243'1, 32'1_4, 32'41, 413'2, 42'13, 42'3'1. The permutations are given in one line notation. The components are separated by _ and the fixed points that are not splitters are marked by '.
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MATHEMATICA
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nn = 20; p = Sum[n! x^n, {n, 0, nn}]; i = 1 - 1/p; CoefficientList[Series[p - x/(1 - i)^2, {x, 0, nn}], x]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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