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Search: id:A050165
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| A050165 |
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T(n,k)=M(2n+1,k,-1), 0<=k<=n, n >= 0, array M as in A050144. |
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+0
4
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| 1, 1, 1, 1, 3, 2, 1, 5, 9, 5, 1, 7, 20, 28, 14, 1, 9, 35, 75, 90, 42, 1, 11, 54, 154, 275, 297, 132, 1, 13, 77, 273, 637, 1001, 1001, 429, 1, 15, 104, 440, 1260, 2548, 3640, 3432, 1430, 1, 17, 135, 663, 2244, 5508, 9996, 13260, 11934
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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T is a mirror image of the array in A039599.
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FORMULA
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Triangle T(n, k) read by rows; given by [1, 0, 0, 0, 0, 0, 0, 0, ...] DELTA [1, 1, 1, 1, 1, 1, 1, 1, 1, ...] where DELTA is the operator defined in A084938. T(n, k) = C(2n, k)*(2n-2k+1)/(2n-k+1) . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Dec 07 2003
Sum_{k=0 ..inf(m, n)} T(m, m-k)*T(n, n-k)= A000108(m+n); A000108: Catalan numbers. - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Dec 30 2003
T(n, k) = 0 if n<k, T(n, n)= A000108(n) and for n>k : T(n, k) = Sum_{j=0..k} T(n-1-j, k-j)*A000108(j+1) . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Feb 03 2004
T(n,k)= Sum_{j, j>=0} (-1)^(n-j)*A094385(n,j)*binomial(j,k) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), May 05 2007
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EXAMPLE
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Rows: {1}; {1,1}; {1,3,2}; ...
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CROSSREFS
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Cf. A084938.
Sequence in context: A077976 A021912 A114597 this_sequence A033878 A144061 A085792
Adjacent sequences: A050162 A050163 A050164 this_sequence A050166 A050167 A050168
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KEYWORD
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nonn,tabl
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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