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A158815
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Triangle T(n,k) read by rows, matrix product of A046899(row-reversed) * A130595.
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3
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1, 1, 1, 4, 1, 1, 13, 5, 1, 1, 46, 16, 6, 1, 1, 166, 58, 19, 7, 1, 1, 610, 211, 71, 22, 8, 1, 1, 2269, 781, 261, 85, 25, 9, 1, 1, 8518, 2920, 976, 316, 100, 28, 10, 1, 1, 32206, 11006, 3676, 1196, 376, 116, 31, 11, 1
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OFFSET
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0,4
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COMMENTS
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The left factor of the matrix product is the triangle which starts
1;
2,1;
6,3,1;
20,10,4,1;
a row-reversed version of A046899, equivalent to the triangular view of the array A092392. The right factor is the inverse of the matrix A007318, which is A130595.
Swapping the two factors, A007318^(-1) * A046899(row-reversed) would generate A158793.
Riordan array (f(x), g(x)) where f(x) is the g.f. of A026641 and where g(x) is the g.f. of A000957. [From Philippe Deléham, Dec 05 2009]
T(n,k)=number of nonnegative paths consisting of upsteps U=(1,1) and downsteps D=(1,-1) of length 2n with k low peaks. (A low peak has its peak vertex at height 1.)
Example: T(3,1)=5 counts UDUUUU, UDUUUD, UDUUDU, UDUUDD, UUDDUD. - David Callan Nov 21 2011
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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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sum_{k=0..n} T(n,k) = A046899(n).
T(n,0)=A026641(n).
Sum_{k, 0<=k<=n} T(n,k)*x^k = A026641(n), A000984(n), A001700(n), A000302(n) for x = 0,1,2,3 respectively. [From Philippe Deléham, Dec 03 2009]
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EXAMPLE
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The triangle starts
1;
1, 1;
4, 1, 1;
13, 5, 1, 1;
46, 16, 6, 1, 1;
166, 58, 19, 7, 1, 1;
610, 211, 71, 22, 8, 1, 1;
2269, 781, 261, 85, 25, 9, 1, 1;
8518, 2620, 976, 316, 100, 28, 10, 1, 1;
32206, 11006, 3676, 1196, 376, 116, 31, 11, 1, 1;
122464, 41746, 13938, 4544, 1442, 441, 133, 34, 12, 1, 1;
...
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CROSSREFS
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Cf. A046899, A000984, A026641, A158793.
Sequence in context: A181145 A227203 A140070 * A101275 A039755 A247502
Adjacent sequences: A158812 A158813 A158814 * A158816 A158817 A158818
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KEYWORD
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nonn,tabl
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AUTHOR
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Gary W. Adamson & Roger L. Bagula, Mar 27 2009
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STATUS
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approved
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