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A102365
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Triangle T(n,k), 0<=k<=n, read by rows: given by [ 1, 0, 3, 0, 5, 0, 7, 0, 9, 0, ...] DELTA [ 0, 1, 0, 2, 0, 3, 0, 4, 0, 5, 0, ...] where DELTA is the operator defined in A084938.
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0
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1, 1, 0, 1, 1, 0, 1, 5, 1, 0, 1, 18, 15, 1, 0, 1, 58, 129, 37, 1, 0, 1, 179, 877, 646, 83, 1, 0, 1, 543, 5280, 8030, 2685, 177, 1, 0, 1, 1636, 29658, 82610, 56285, 10002, 367, 1, 0, 1, 4916, 159742, 756218, 919615, 335162, 34777, 749, 1, 0
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,8
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COMMENTS
| Generalized Eulerian numbers A008292.
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FORMULA
| T(n, k) = (n-k)*T(n-1, k-1) + (2*k+1)*T(n-1, k) with T(0, 0) = 1, T(0, k) = 0 if k>0, T(n, k) = 0 if k<0.
Sum_{k>=0} T(n, k)*2^k = A001147(n).
Sum_{k>=0} T(n, k) = A014307(n) . - Philippe DELEHAM, Mar 19 2005
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EXAMPLE
| 1; 1, 0; 1, 1, 0; 1, 5, 1, 0; 1, 18, 15, 1, 0; 1, 58, 129, 37, 1, 0; ...
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CROSSREFS
| Diagonals : A000012, A000340; A000007, A000012, A050488.
Sequence in context: A019755 A085475 A157012 * A102259 A021200 A019904
Adjacent sequences: A102362 A102363 A102364 * A102366 A102367 A102368
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KEYWORD
| nonn,easy,tabl
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AUTHOR
| DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Feb 22 2005
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