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Search: id:A134388
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| A134388 |
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A generalized Riordan array related to Hankel and Toeplitz+Hankel transforms. |
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+0
2
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| 1, 1, 1, 1, 2, 1, 2, 3, 2, 1, 3, 6, 4, 2, 1, 6, 10, 8, 5, 2, 1, 10, 20, 15, 10, 6, 2, 1, 20, 35, 30, 21, 12, 7, 2, 1, 35, 70, 56, 42, 28, 14, 8, 2, 1, 70, 126, 112, 84, 56, 36, 16, 9, 2, 1, 126, 252, 210, 168, 120, 72, 45, 18, 10, 2, 1
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Corresponds to the Riordan array ((1+2x)/sqrt(1-4x^2),xc(x^2)), c(x) the g.f. of A000108, with the first column replaced by 1,1,1,2,3,6,... with g.f. (1+2x+sqrt(1-4x^2))/(2*sqrt(1-4x^2)). Alternatively it is the array with first column 1,1,1,2,3,6,... and then the Riordan array ((1+2x)c(x)/sqrt(1-4x^2),xc(x^2)) embedded from the (1,1) position (indexing starting at (0,0)). Row sums are 2^n. Images of common sequences under this array have interesting Hankel transforms. For instance, the image of r^n has Hankel transform with g.f. 1/(1+(r^2-1)x^2).
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REFERENCES
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E.L. Basor, T. Erhardt, Some identities for determinants of structured matrices, arXiv:math/0008075v1
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EXAMPLE
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Triangle begins
1,
1, 1,
1, 2, 1,
2, 3, 2, 1,
3, 6, 4, 2, 1,
6, 10, 8, 5, 2, 1,
10, 20, 15, 10, 6, 2, 1,
20, 35, 30, 21, 12, 7, 2, 1,
35, 70, 56, 42, 28, 14, 8, 2, 1,
70, 126, 112, 84, 56, 36, 16, 9, 2, 1,
126, 252, 210, 168, 120, 72, 45, 18, 10, 2, 1
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CROSSREFS
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Sequence in context: A109814 A133088 A059982 this_sequence A055095 A048685 A101050
Adjacent sequences: A134385 A134386 A134387 this_sequence A134389 A134390 A134391
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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), Oct 23 2007
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