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A172250
Triangle, read by rows, given by [0,1,-1,0,0,0,0,0,0,0,...] DELTA [1,-1,1,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938.
2
1, 0, 1, 0, 1, 0, 0, 0, 2, -1, 0, 0, 1, 1, -1, 0, 0, 0, 3, -2, 0, 0, 0, 0, 1, 3, -4, 1, 0, 0, 0, 0, 4, -2, -2, 1, 0, 0, 0, 0, 1, 6, -9, 3, 0, 0, 0, 0, 0, 0, 5, 0, -9, 6, -1, 0, 0, 0, 0, 0, 1, 10, -15, 3, 3, -1, 0, 0, 0, 0, 0, 0, 6, 5, -24, 18, -4, 0, 0, 0, 0, 0, 0, 0, 1, 15, -20, -6, 18, -8, 1
OFFSET
0,9
FORMULA
T(n,k) = T(n-1,k-1) + T(n-2,k-1) - T(n-2,k-2), T(0,0)=1, T(n,k) = 0 if k > n or if k < 0.
Sum_{k=0..n} T(n,k)*x^k = (-1)^n*A088139(n+1), A001607(n+1), A000007(n), A000012(n), A099087(n), A190960(n+1) for x = -2, -1, 0, 1, 2, 3 respectively. - Philippe Deléham, Feb 15 2012
G.f.: 1/(1-y*x+y*(y-1)*x^2). - Philippe Deléham, Feb 15 2012
EXAMPLE
Triangle begins:
1;
0, 1;
0, 1, 0;
0, 0, 2, -1;
0, 0, 1, 1, -1;
0, 0, 0, 3, -2, 0;
0, 0, 0, 1, 3, -4, 1;
0, 0, 0, 0, 4, -2, -2, 1; ...
CROSSREFS
Cf. A101950.
Sequence in context: A115201 A354100 A118229 * A309047 A255317 A309168
KEYWORD
sign,tabl
AUTHOR
Philippe Deléham, Jan 29 2010
STATUS
approved