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A122935
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.
1
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
OFFSET
0,9
COMMENTS
Subtriangle (1 <= k <= n) is in A056241.
FORMULA
T(2*k-1,k) = A082758(k-1)for k >= 1.
Sum_{k=0..n} T(n,k) = A124302(n); see also A007051.
Sum_{k=0..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). - Philippe Deléham, Oct 30 2011
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;
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Philippe Deléham, Oct 30 2006
STATUS
approved