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A122935
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Triangle T(n,k), 0<=k<=n, read by rows given by [0, 1, 0, 1, 0, 0, 0, 0, 0, ...] DELTA [1, 0, 1, 0, 0, 0, 0, 0, 0, ...] where DELTA is the operator defined in A084938.
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1
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1, 0, 1, 0, 1, 1, 0, 1, 3, 1, 0, 1, 6, 6, 1, 0, 1, 10, 19, 10, 1, 0, 1, 15, 45, 45, 15, 1, 0, 1, 21, 90, 141, 90, 21, 1, 0, 1, 28, 161, 357, 357, 161, 28, 1, 0, 1, 36, 266, 784, 1107, 784, 266, 36, 1, 0, 1, 45, 414, 1554, 2907, 2907, 1554, 414, 45, 1, 0, 1, 55, 615, 2850, 6765, 8953
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,9
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COMMENTS
| Subtriangle (1<=k<=n)is in A056241.
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FORMULA
| T(2*k-1,k)=A082758(k-1)for k>=1 . Sum_{k, 0<=k<=n}T(n,k)=A124302(n), see also A007051 . Sum_{k, 0<=k<=n}(-1)^(n-k)*T(n,k)=A117569(n).
G.f.: (1-x*(y+2)+x^2)/(1-2x*(1+y)+(1+y+y^2)*x^2). - From DELEHAM Philippe, Oct 30 2011
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EXAMPLE
| Triangle begins:
1;
0, 1;
0, 1, 1;
0, 1, 3, 1;
0, 1, 6, 6, 1;
0, 1, 10, 19, 10, 1;
0, 1, 15, 45, 45, 15, 1;
0, 1, 21, 90, 141, 90, 21, 1;
0, 1, 28, 161, 357, 357, 161, 28, 1;
0, 1, 36, 266, 784, 1107, 784, 255, 36, 1;
0, 1, 45, 414, 1554, 2907, 2907, 1554, 414, 45, 1;
0, 1, 55, 615, 2850, 6765, 8953, 6765, 2850, 615, 55, 1;
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CROSSREFS
| Columns are : A000007, A000012, A000217, A005712, A005714, A005716 Cf. A027907, A056241.
Sequence in context: A098157 A165253 A059045 * A131198 A090181 A144417
Adjacent sequences: A122932 A122933 A122934 * A122936 A122937 A122938
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KEYWORD
| nonn,tabl
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AUTHOR
| Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 30 2006
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