A132815 A007318^(-1) * A132814.

1, -1, 2, 1, -2, 3, -1, 0, 0, 4, 1, 4, -12, 8, 5, -1, -10, 30, -40, 25, 6, 1, 18, -45, 60, -75, 54, 7, -1, -28, 42, 0, 0, -84, 98, 8, 1, 40, 0, -224, 420, -336, 0, 160, 9, -1, -54, -108, 672, -1260, 1512, -1176, 288, 243, 10

Offset: 0

Author

Gary W. Adamson, Sep 01 2007

Keywords

• tabl
• easy
• sign

Comments

Row sums = A001405: (1, 1, 2, 3, 6, 10, 10, ...).

Examples

			First few rows of the triangle:
   1;
  -1,   2;
   1,  -2,   3;
  -1,   0,   0,    4;
   1,   4, -12,    8,   5;
  -1, -10,  30, -240,  25,  6;
   1,  18, -45,   60, -75, 54, 7;
  ...
		

Crossrefs

Cf. A001405, A007318, A132814.

Programs

PARI

tabl(nn) = {t007318 = matrix(nn, nn, n, k, binomial(n-1, k-1)); t132813 = matrix(nn, nn, n, k, binomial(n-1, k-1)*binomial(n, k-1)); t132814 = t007318^(-1)*t132813; t132815 = t007318^(-1)*t132814; for (n=1, nn, for (k=1, n, print1(t132815[n, k], ", ");););} \\ Michel Marcus, Feb 12 2014

Formula

Inverse binomial transform of A132814.

Extensions

Typo corrected by Travis Hoppe, Apr 24 2008

T(5, 1) corrected by Michel Marcus, Feb 12 2014