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Search: id:A091186
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| A091186 |
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Triangle read by rows, in which n-th row gives expansion of x^n/((1-x)(1-x-x^2)^n). |
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+0
2
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| 1, 1, 1, 1, 2, 1, 1, 4, 3, 1, 1, 7, 8, 4, 1, 1, 12, 18, 13, 5, 1, 1, 20, 38, 35, 19, 6, 1, 1, 33, 76, 86, 59, 26, 7, 1, 1, 54, 147, 197, 164, 91, 34, 8, 1, 1, 88, 277, 430, 420, 281, 132, 43, 9, 1, 1, 143, 512, 904, 1014, 792, 447, 183, 53, 10, 1, 1, 232, 932, 1846, 2338, 2087, 1371
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Riordan array (1/(1-x),x/(1-x-x^2)). - Paul Barry (pbarry(AT)wit.ie), Sep 13 2006
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FORMULA
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G.f.: (1-y-y^2) / [(1-y(1+y+z))(1-y)].
Number triangle T(n,k)=sum{j=0..n-k, sum{i=0..n-k-j, C(k+j-1,j)C(j,n-k-i-j)}}; - Paul Barry (pbarry(AT)wit.ie), Sep 13 2006
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EXAMPLE
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Rows begin {1},{1,1},{1,2,1},{1,4,3,1}...
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CROSSREFS
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Row sums are A024537. Diagonal sums are A005578. Second column is A000071. Third column is A006478.
Essentially the vertical partial sums of triangle A037027.
Sequence in context: A058717 A034371 A101321 this_sequence A138155 A055587 A137743
Adjacent sequences: A091183 A091184 A091185 this_sequence A091187 A091188 A091189
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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), Dec 25 2003
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