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A067345
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Square array read by antidiagonals: T(n,k)=(T(n,k-1)*n^2-Catalan(k-1))/(n-1) with a(n,1)=1 and a(1,k)=Catalan(k) where Catalan(k)=C(2k,k)/(k+1)=A000108(k).
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3
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1, 2, 1, 5, 3, 1, 14, 10, 4, 1, 42, 35, 17, 5, 1, 132, 126, 74, 26, 6, 1, 429, 462, 326, 137, 37, 7, 1, 1430, 1716, 1446, 726, 230, 50, 8, 1, 4862, 6435, 6441, 3858, 1434, 359, 65, 9, 1, 16796, 24310, 28770, 20532, 8952, 2582, 530, 82, 10, 1, 58786, 92378, 128750
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OFFSET
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1,2
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COMMENTS
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Also table given by Sum_{k, 0<=k<=n}A039598(n,k)*x^k ; table begins : x=0 : 1, 2, 5, 42, 132, ...(see A000108); x=1 : 1, 3, 10, 35, 126, ...(see A001700); x=2 : 1, 4, 17, 74, 326, ...(see A049027); x=3 : 1, 5, 26, 137, 726, ...(see A075025); x=4 : 1, 6, 37, 230, 1434, ...(see A075026); x=5 : 1, 7, 50, 359, 2582, ... - Philippe Deléham, Mar 21 2007
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LINKS
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Table of n, a(n) for n=1..58.
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FORMULA
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T(n, k) =A067346(n, k)/(n-1) =A067347(n, k)/n
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CROSSREFS
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Rows include A000108, A001700, A049027. Columns essentially include A000012, A000027, A002522.
Sequence in context: A054445 A105848 A048471 * A242431 A349934 A188416
Adjacent sequences: A067342 A067343 A067344 * A067346 A067347 A067348
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KEYWORD
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nonn,tabl
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AUTHOR
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Henry Bottomley, Jan 16 2002
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STATUS
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approved
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