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Search: id:A111805
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| A111805 |
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Number triangle T(n,k)=binomial(2(n+k),4k). |
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1
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| 1, 1, 1, 1, 15, 1, 1, 70, 45, 1, 1, 210, 495, 91, 1, 1, 495, 3003, 1820, 153, 1, 1, 1001, 12870, 18564, 4845, 231, 1, 1, 1820, 43758, 125970, 74613, 10626, 325, 1, 1, 3060, 125970, 646646, 735471, 230230, 20475, 435, 1, 1, 4845, 319770, 2704156, 5311735
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Related to matchings of the complete graph K_2n: T(n,k)=A100861(2(n+k),2k)/f(2k), where f(n)=(2n-1)!! Column k gives number of standard tableaux of shape (2n+1,1^(4k)).
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FORMULA
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Column k has g.f. x^k*sum{j=0..2k+1, binomial(4k+1, 2j)x^j}/(1-x)^(4k+1)
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EXAMPLE
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Rows begin
1;
1,1;
1,15,1;
1,70,45,1;
1,210,495,91,1;
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CROSSREFS
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Sequence in context: A040226 A040225 A070644 this_sequence A022178 A015139 A040231
Adjacent sequences: A111802 A111803 A111804 this_sequence A111806 A111807 A111808
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Aug 17 2005
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