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A092392
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Array read by antidiagonals: T(k,n) = C(2n+k,n).
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11
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1, 2, 1, 6, 3, 1, 20, 10, 4, 1, 70, 35, 15, 5, 1, 252, 126, 56, 21, 6, 1, 924, 462, 210, 84, 28, 7, 1, 3432, 1716, 792, 330, 120, 36, 8, 1, 12870, 6435, 3003, 1287, 495, 165, 45, 9, 1, 48620, 24310, 11440, 5005, 2002, 715, 220, 55, 10, 1, 184756, 92378, 43758
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| First column is C(2n,n) or A000984. Central coefficients are C(3n,n) or A005809. [From Paul Barry (pbarry(AT)wit.ie), Oct 14 2009]
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LINKS
| V. J. W. Guo and J. Zeng, The number of convex polyominoes and the generating function of Jacobi polynomials, Lemma 4.
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FORMULA
| As a number triangle, this is T(n, k)=if(k<=n, C(2n-k, n), 0). Its row sums are C(2n+1, n+1)=A001700. Its diagonal sums are A176287. - Paul Barry (pbarry(AT)wit.ie), Apr 23 2005
G.f.: 2^k/[sqrt(1-4x)*(1+sqrt(1-4x))^k].
As a number triangle, this is the Riordan array (1/sqrt(1-4x), xc(x)), c(x) the g.f. of A000108. - Paul Barry (pbarry(AT)wit.ie), Jun 24 2005
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EXAMPLE
| Contribution from Paul Barry (pbarry(AT)wit.ie), Oct 14 2009: (Start)
Triangle begins
1,
2, 1,
6, 3, 1,
20, 10, 4, 1,
70, 35, 15, 5, 1,
252, 126, 56, 21, 6, 1,
924, 462, 210, 84, 28, 7, 1,
3432, 1716, 792, 330, 120, 36, 8, 1
Production array is
2, 1,
2, 1, 1,
2, 1, 1, 1,
2, 1, 1, 1, 1,
2, 1, 1, 1, 1, 1,
2, 1, 1, 1, 1, 1, 1,
2, 1, 1, 1, 1, 1, 1, 1,
2, 1, 1, 1, 1, 1, 1, 1, 1,
2, 1, 1, 1, 1, 1, 1, 1, 1, 1 (End)
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CROSSREFS
| Rows 0-14 are A000984, A001700, A001791, A002054, A002694, A003516, A002696, A030053, A004310, A030054, A004311, A030055, A004312, A030056, A004313.
Columns are A000217, A000292, A000332, A000389, A000579.
Diagonals are A005809, A045721, A025174, A004319, A013698, A003408.
Sequence in context: A168151 A180281 A187888 * A128741 A175757 A060539
Adjacent sequences: A092389 A092390 A092391 * A092393 A092394 A092395
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KEYWORD
| nonn,tabl
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AUTHOR
| Ralf Stephan (ralf(AT)ark.in-berlin.de), Mar 21 2004
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EXTENSIONS
| Diagonal sums comment corrected Paul Barry (pbarry(AT)wit.ie), Apr 14 2010
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