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Search: id:A110519
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| A110519 |
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Riordan array (1/(1-xc(3x)),xc(3x)/(1-xc(3x))), c(x) the g.f. of A000108. |
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+0
6
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| 1, 1, 1, 4, 5, 1, 25, 33, 9, 1, 190, 256, 78, 13, 1, 1606, 2186, 703, 139, 17, 1, 14506, 19863, 6591, 1430, 216, 21, 1, 137089, 188449, 63813, 14669, 2501, 309, 25, 1, 1338790, 1845416, 633808, 151532, 27940, 3980, 418, 29, 1, 13403950, 18513822
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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Product of (1,xc(3x)) and (1/(1-x),x/(1-x)) (A110518 and A007318). The binomial transform of the inverse of this triangle has general element (-3)^(n-k)*C(k,n-k), that is, it is the Riordan array (1,x(1-3x)) [A110517]. Row sums are A110520. Diagonal sums are A110521.
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FORMULA
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Number triangle T(0, k)=0^k, T(n, k)=sum{j=0..n, j*C(2n-j-1, n-j)C(j, k)3^(n-j)/n}, n, k>0. Deleham triangle Delta(0^n, 3-2*0^n) [see construction in A084938].
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EXAMPLE
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Rows begin
1;
1,1;
4,5,1;
25,33,9,1;
190,256,78,13,1;
1606,2186,703,139,17,1;
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CROSSREFS
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Sequence in context: A108446 A109962 A102230 this_sequence A113095 A016715 A085548
Adjacent sequences: A110516 A110517 A110518 this_sequence A110520 A110521 A110522
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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), Jul 24 2005
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