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Search: id:A140638
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| A140638 |
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Number of labeled complex components with n nodes. |
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+0
1
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| 0, 0, 0, 7, 381, 21748, 1781154, 249849880, 66257728763, 34495508486976, 35641629989151608
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OFFSET
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1,4
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COMMENT
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From A129137, for n >= 3, and N = n-3, we get A057500(n) = binom(n-1,2)Sum_{r=0..N}n^{N-r}(N)_r, noting that
for r = 1, (n-3)!/(n-2-1)! = (n-3)_0 = (N)_0,
for r = 2, (n-3)!/(n-2-2)! = n-3 = (N)_1,
...
for r = n-3, (n-3)!/(n-2-(n-3))! = (n-3)! = (N)_(n-2), and
for r = n-2, (n-3)!/(n-2-(n-2))! = (n-3)! = (N)_N.
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REFERENCES
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J. Riordan, An Introduction to Combinatorial Analysis, Dover, 2002, p. 2.
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FORMULA
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a(n) = A001187(n) - A000272(n) - A057500(n). For n >= 3, a(n)= A001187(n) - n^(n-2) - binom(n-1,2)Sum_{r=0..N}n^{N-r}(N)_r; N = n-3.
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EXAMPLE
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a(5) = 381 because A001187(5) = 728, N = 2, and
Sum_{r=0..N}n^{N-r}(N)_r = 5^{2-0}(2)_0 + 5^{2-1}(2)_1 + 5^{2-2}(2)_2 =
25 + 10 + 2 = 37. So we get 728 - 125 - 6*37.
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CROSSREFS
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Cf. A000272, A001187, A057500, A129137, A140636.
Sequence in context: A084001 A073908 A027510 this_sequence A112905 A058275 A009712
Adjacent sequences: A140635 A140636 A140637 this_sequence A140639 A140640 A140641
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KEYWORD
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easy,nonn,uned
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AUTHOR
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Washington Bomfim (webonfim(AT)bol.com.br), May 21 2008
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