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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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3
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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
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OFFSET
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0,5
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COMMENTS
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T is a mirror image of the array in A039599.
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LINKS
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Table of n, a(n) for n=0..53.
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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) . - Philippe Deléham, Dec 07 2003
Sum_{k=0 ..inf(m, n)} T(m, m-k)*T(n, n-k)= A000108(m+n); A000108: Catalan numbers. - Philippe Deléham, 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) . - Philippe Deléham, Feb 03 2004
T(n,k)= Sum_{j, j>=0} (-1)^(n-j)*A094385(n,j)*binomial(j,k) . - Philippe DELEHAM, May 05 2007
T(2n,n) = A126596(n) . - From Philippe Deléham, Nov 23 2011
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EXAMPLE
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Rows: {1}; {1,1}; {1,3,2}; ...
Triangle begins :
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
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CROSSREFS
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Cf. A039599, A084938.
Sequence in context: A021912 A114597 A199479 * A198876 A033878 A144061
Adjacent sequences: A050162 A050163 A050164 * 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
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STATUS
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approved
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