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A114117 Inverse of 1's counting matrix A114116. 2
1, 0, 1, -2, 1, 1, -1, -1, 1, 1, 0, -2, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, 0, -2, 0, 0, 1, 1, 0, 0, -1, -1, 0, 0, 1, 1, 0, 0, 0, -2, 0, 0, 0, 1, 1, 0, 0, 0, -1, -1, 0, 0, 0, 1, 1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
Row sums are (1,1,0,0,0,.....) with g.f. 1+x. Diagonal sums have g.f. (1-x^2-x^3)/(1-x^3). Product of A114115 and the first difference matrix (1-x,x).
LINKS
FORMULA
T(n, k)=sum{j=0..n, sum{i=0..n, C(floor((n+i)/2, j)C(j, floor((n+i)/2))}*(2*C(0, j-k)-C(1, j-k))}}.
EXAMPLE
Triangle begins
1;
0, 1;
-2, 1, 1;
-1,-1, 1, 1;
0,-2, 0, 1, 1;
0,-1,-1, 0, 1, 1;
0, 0,-2, 0, 0, 1, 1;
0, 0,-1,-1, 0, 0, 1, 1;
CROSSREFS
Sequence in context: A162781 A056975 A294079 * A144435 A182533 A173120
KEYWORD
easy,sign,tabl
AUTHOR
Paul Barry, Nov 13 2005
STATUS
approved

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Last modified March 1 11:28 EST 2024. Contains 370432 sequences. (Running on oeis4.)