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Search: id:A124926
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| A124926 |
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Triangle read by rows: T(n,k)=binom(n,k)*r(k), where r(k) are the Riordan numbers (r(k)=A005043(k); 0<=k<=n). |
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2
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| 1, 1, 0, 1, 0, 1, 1, 0, 3, 1, 1, 0, 6, 4, 3, 1, 0, 10, 10, 15, 6, 1, 0, 15, 20, 45, 36, 15, 1, 0, 21, 35, 105, 126, 105, 36, 1, 0, 28, 56, 210, 336, 420, 288, 91, 1, 0, 36, 84, 378, 756, 1260, 1296, 819, 232, 1, 0, 45, 120, 630, 1512, 3150, 4320, 4095, 2320, 603, 1, 0, 55, 165
(list; table; graph; listen)
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OFFSET
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0,9
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COMMENT
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Row sums = Catalan numbers, A000108: (1, 1, 2, 5, 14, 42...); e.g. sum of row 4 terms = A000108(4) = 14 = (1 + 0 + 6 + 4 + 3). A005043 is the inverse binomial transform of the Catalan numbers.
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EXAMPLE
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First few rows of the triangle are:
1;
1, 0;
1, 0, 1;
1, 0, 3, 1;
1, 0, 6, 4, 3;
1, 0, 10, 10, 15, 6;
1, 0, 15, 20, 45, 36, 15;
...
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MAPLE
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r:=n->(1/(n+1))*sum((-1)^i*binomial(n+1, i)*binomial(2*n-2*i, n-i), i=0..n): T:=(n, k)->r(k)*binomial(n, k): for n from 0 to 11 do seq(T(n, k), k=0..n) od; # yields sequence in triangular form
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CROSSREFS
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Cf. A005043, A000108.
Sequence in context: A130160 A162169 A124801 this_sequence A115378 A120060 A143295
Adjacent sequences: A124923 A124924 A124925 this_sequence A124927 A124928 A124929
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KEYWORD
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nonn,tabl
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 12 2006
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com), Nov 29 2006
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