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Search: id:A136128
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| A136128 |
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Number of components in all permutations of [1,2,...,n]. |
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+0
1
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| 1, 3, 10, 40, 192, 1092, 7248, 55296, 478080, 4625280, 49524480, 581368320, 7422589440, 102372076800, 1516402944000, 24004657152000, 404347023360000, 7220327288832000, 136227009945600000, 2707657158721536000
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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a(n)=A003149(n)-n!; a(n)=A059371(n)+n! (n>=2); a(n)=Sum(k*A059438(n,k),k=1..n)
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REFERENCES
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L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 262 (#14).
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FORMULA
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a(n)=Sum(i!*(n-i)!, i=0..n-1). a(n)=(n+1)![1+Sum(2^j/(j+1),j=1..n-1)]/2^n. Rec. rel.; a(n)=(n+1)a(n-1)/2 +(n-1)!(n+1)/2; a(1)=1. G.f.=f(f-1), where f(x)=Sum(j!x^j,j>=0).
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EXAMPLE
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a(3)=10 because the permutations of [1,2,3], with components separated by /, are 1/2/3, 1/32, 21/3, 231, 312, and 321.
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MAPLE
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seq(add(factorial(i)*factorial(n-i), i=0..n-1), n=1..20);
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CROSSREFS
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Cf. A059438, A003149, A059371.
Adjacent sequences: A136125 A136126 A136127 this_sequence A136129 A136130 A136131
Sequence in context: A151076 A151077 A003703 this_sequence A089902 A093133 A030817
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 21 2008
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