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Search: id:A067057
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| A067057 |
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Let A(n) = {1,2,3,...n}. Let B(r) and C(n-r) be two subsets of A(n) having r and n-r elements respectively, such that B(r) U C(n-r) = A(n) and B and C are disjoint; then a(n) = sum of the products of all combination sums of elements of B and C for r =1 to n-1. |
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1
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| 0, 2, 22, 140, 680, 2800, 10304, 34944, 111360, 337920, 985600, 2782208, 7641088, 20500480, 53903360, 139264000, 354287616, 889061376
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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For n>1, all listed values are given by a(n)=(2^(n-2))*s(n+1, n-1), where the s(n+1, n-1) are Stirling numbers of the first kind (A000914). - John W. Layman (layman(AT)math.vt.edu), Jan 05 2002
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EXAMPLE
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a(4) = (1)*(2+3+4) + 2*(1+3+4) + 3*(1+2+4) + 4(1+2+3) +(1+2)*(3+4) + (1+3)*(2+4) +(1+4)*(2+3) = 140.
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CROSSREFS
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Cf. A000914.
Sequence in context: A105237 A083833 A062180 this_sequence A084399 A123960 A091169
Adjacent sequences: A067054 A067055 A067056 this_sequence A067058 A067059 A067060
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jan 02 2002
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EXTENSIONS
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More terms and formula from John W. Layman (layman(AT)math.vt.edu), Jan 05 2002
Corrected by Franklin T. Adams-Watters and T. D. Noe (noe(AT)sspectra.com), Oct 25 2006
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