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A110488
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A number triangle based on the Catalan numbers.
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2
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1, 1, 1, 2, 2, 1, 5, 5, 3, 1, 14, 14, 10, 4, 1, 42, 42, 35, 17, 5, 1, 132, 132, 126, 74, 26, 6, 1, 429, 429, 462, 326, 137, 37, 7, 1, 1430, 1430, 1716, 1446, 726, 230, 50, 8, 1, 4862, 4862, 6435, 6441, 3858, 1434, 359, 65, 9, 1, 16796, 16796, 24310, 28770, 20532, 8952
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Columns include A000108,A001700,A049027(n+1),A076025(n+1). Rows sums are A110489, diagonal sums are A110490.
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FORMULA
| T(n, k)=sum{j=0..n-k, (k-1)^j*C(2(n-k)+1, n-k-j)*2*(j+1)/(n-k+j+2)}; Column k has g.f. x^k*c(x)/(1-k*x*c(x)) where c(x) is the g.f. of A000108.
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EXAMPLE
| Rows begin
1;
1,1;
2,2,1;
5,5,3,1;
14,14,10,4,1;
42,42,35,17,5,1;
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CROSSREFS
| Sequence in context: A079222 A033184 A171567 * A134379 A108087 A123158
Adjacent sequences: A110485 A110486 A110487 * A110489 A110490 A110491
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Jul 22 2005
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