A133088 A007318^(-1) * A133080.

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

Author

Gary W. Adamson, Sep 08 2007

Keywords

• tabl
• sign

Comments

Row sums give A123344.

Inverse binomial transform of A133080.

Examples

			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;
  ...
		

Crossrefs

Cf. A133080, A007318.

Programs

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

Extensions

Typo corrected by Travis Hoppe, Apr 24 2008

One term's sign corrected by Michel Marcus, Feb 13 2014