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A133088
A007318^(-1) * A133080.
0
1, 0, 1, -1, -2, 1, 2, 3, -2, 1, -3, -4, 2, -4, 1, 4, 5, 0, 10, -4, 1, -5, -6, -5, -20, 9, -6, 1, 6, 7, 14, 35, -14, 21, -6, 1, -7, -8, -28, -56, 14, -56, 20, -8, 1, 8, 9, 48, 84, 0, 126, -48, 36, -8, 1, -9, -10, -75, -120, -42, -252, 90, -120, 35, -10, 1
OFFSET
0,5
COMMENTS
Row sums give A123344.
Inverse binomial transform of A133080.
EXAMPLE
First few rows of the triangle:
1;
0, 1;
-1, -2, 1;
2, 3, -2, 1;
-3, -4, 2, -4, 1;
4, 5, 0, 10, -4, 1;
-5, -6, -5, -20, 9, -6, 1;
...
PROG
(PARI) tabl(nn) = {t007318 = matrix(nn, nn, n, k, binomial(n-1, k-1)); t133080 = matrix(nn, nn, n, k, if (k==n, 1, if (k == (n-1), 1 - (n % 2), 0))); t133088 = t007318^(-1)*t133080; for (n = 1, nn, for (k = 1, n, print1(t133088[n, k], ", "); ); print(); ); } \\ Michel Marcus, Feb 13 2014
CROSSREFS
Sequence in context: A355248 A111944 A109814 * A059982 A187801 A134388
KEYWORD
tabl,sign
AUTHOR
Gary W. Adamson, Sep 08 2007
EXTENSIONS
Typo corrected by Travis Hoppe, Apr 24 2008
One term's sign corrected by Michel Marcus, Feb 13 2014
STATUS
approved