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A122960
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Triangle T(n,k), 0<=k<=n, read by rows given by [0, 1, -1, -1, 1, 0, 0, 0, 0, 0, 0, ...] DELTA [1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, ...] where DELTA is the operator defined in A084938.
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0
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1, 0, 1, 0, 1, 1, 0, 0, 3, 1, 0, 1, 9, 6, 1, 0, 0, 5, 0, 10, 1, 0, 1, 0, 15, 0, 15, 1, 0, 0, 7, 0, 35, 0, 21, 1, 0, 1, 0, 28, 0, 70, 0, 28, 1, 0, 0, 9, 0, 84, 0, 126, 0, 36, 1, 0, 1, 0, 45, 0, 210, 0, 210, 0, 45, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,9
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COMMENTS
| T(n,k)= binomial (n,n-k+1) if (n-k) is an odd number (see A000217, A000332, A000579, A000581, ..). T(n,k)= 0 if (n-k)=2x with x>0 (see A000004).T(n,n)=1 (see A000012).
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FORMULA
| Sum_{k, 0<=k<=n}T(n,k)=A011782(n) . Sum_{k, 0<=k<=n}2^k*T(n,k)=A083323(n) . Sum_{k, 0<=k<=n}2^(n-k)*T(n,k)=A122983(n).
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EXAMPLE
| Triangle begins:
1;
0, 1;
0, 1, 1;
0, 0, 3, 1;
0, 1, 0, 6, 1;
0, 0, 5, 0, 10, 1;
0, 1, 0, 15, 0, 15, 1;
0, 0, 7, 0, 35, 0, 21, 1;
0, 1, 0, 28, 0, 70, 0, 28, 1;
0, 0, 9, 0, 84, 0, 126, 0, 36, 1;
0, 1, 0, 45, 0, 210, 0, 210, 0, 45, 1;
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CROSSREFS
| Cf. A000004, A000012, A000217, A000332, A000579, A000581, A007318.
Sequence in context: A048993 A193357 A112413 * A091480 A034374 A103879
Adjacent sequences: A122957 A122958 A122959 * A122961 A122962 A122963
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KEYWORD
| nonn,tabl
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AUTHOR
| Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 26 2006
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