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A122016
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Riordan array(1,x*(1+2*x)/(1-x)).
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3
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1, 0, 1, 0, 3, 1, 0, 3, 6, 1, 0, 3, 15, 9, 1, 0, 3, 24, 36, 12, 1, 0, 3, 33, 90, 66, 15, 1, 0, 3, 42, 171, 228, 105, 18, 1, 0, 3, 51, 279, 579, 465, 153, 21, 1, 0, 3, 60, 414, 1200, 1500, 828, 210, 24, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Triangle T(n,k), 0<=k<=n, read by rows given by [0,3,-2,0,0,0,0,0,0,...] DELTA [1,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938 . Rising and falling diagonals are A078010 and A122552.
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FORMULA
| Sum_{k, 0<=k<=n}T(n,k)*x^(n-k) = A026150(n), A102900(n) for x = 1, 2.
T(n,k)=T(n-1,k)+T(n-1,k-1)+2*T(n-2,k-1) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 25 2006
G.f.: (1-x)/(1-(y+1)*x-2*y*x^2). - DELEHAM Philippe, Jan 31 2012
Sum_{k, 0<=k<=n} T(n,k)*x^k = A117575(n+1), A000007(n), A026150(n), A122117(n), A147518(n) for x = -1, 0, 1, 2, 3 respectively. - DELEHAM Philippe, Jan 31 2012
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EXAMPLE
| Triangle begins:
1;
0, 1;
0, 3, 1;
0, 3, 6, 1;
0, 3, 15, 9, 1;
0, 3, 24, 36, 12, 1;
0, 3, 33, 90, 66, 15, 1;
0, 3, 42, 171, 228, 105, 18, 1;
0, 3, 51, 279, 579, 465, 153, 21, 1;
0, 3, 60, 414, 1200, 1500, 828, 210, 24, 1;
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CROSSREFS
| Cf. Diagonals A000012, A008585, A062741, columns A000007, A122553, A122709, row sums A026150.
Sequence in context: A049403 A104556 A116089 * A067882 A110033 A166407
Adjacent sequences: A122013 A122014 A122015 * A122017 A122018 A122019
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KEYWORD
| nonn,tabl
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AUTHOR
| Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 24 2006
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