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Search: id:A115112
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| A115112 |
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Number of different ways to select n elements from two sets of n elements under the precondition of choosing at least one element from each set. |
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+0
3
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| 0, 4, 18, 68, 250, 922, 3430, 12868, 48618, 184754, 705430, 2704154, 10400598, 40116598, 155117518, 601080388, 2333606218, 9075135298, 35345263798, 137846528818, 538257874438, 2104098963718, 8233430727598, 32247603683098
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OFFSET
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1,2
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COMMENT
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The number of different ways to select n elements from two sets of n elements under the precondition of choosing at least one element from each set.
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FORMULA
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a(n) = binomial(2*n, n)-2; also: a(n)=sum{binomial(n, i)*binomial(n, j|i, j=1...(n-1), i+j=n}.
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EXAMPLE
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a(5)=binomial(10,5)-2=250.
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MAPLE
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seq(sum((binomial(n, m))^2, m=1..n-1), n=1..24); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 19 2008
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CROSSREFS
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Cf. A000984, A115246, A115111.
Sequence in context: A100177 A083321 A022728 this_sequence A005367 A050184 A034352
Adjacent sequences: A115109 A115110 A115111 this_sequence A115113 A115114 A115115
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KEYWORD
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nonn
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AUTHOR
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Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jan 22 2006
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