A127755 Inverse of number triangle A(n,k) = 1/n! if k <= n <= 2k, 0 otherwise.

1, 0, 1, 0, -1, 2, 0, 1, -2, 6, 0, 0, 0, -6, 24, 0, -1, 2, 0, -24, 120, 0, 0, 0, 0, 0, -120, 720, 0, 1, -2, 6, 0, 0, -720, 5040, 0, 0, 0, 0, 0, 0, 0, -5040, 40320, 0, 0, 0, -6, 24, 0, 0, 0, -40320, 362880, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 0

Author

Paul Barry, Jan 28 2007

Keywords

• sign
• tabl

Comments

It is conjectured that this is an integer triangle. Row sums are A127756.

Examples

			Triangle begins
  1;
  0,  1;
  0, -1,  2;
  0,  1, -2,  6;
  0,  0,  0, -6,  24;
  0, -1,  2,  0, -24,  120;
  0,  0,  0,  0,   0, -120,  720;
  0,  1, -2,  6,   0,    0, -720,  5040;
  0,  0,  0,  0,   0,    0,    0, -5040,  40320;
  0,  0,  0, -6,  24,    0,    0,     0, -40320,  362880;
  0,  0,  0,  0,   0,    0,    0,     0,      0, -362880,  3628800;
  0, -1,  2,  0, -24,  120,    0,     0,      0,       0, -3628800,  39916800;
  0,  0,  0,  0,   0,    0,    0,     0,      0,       0,        0, -39916800, 479001600;
Inverse of triangle begins
  1;
  0,  1;
  0, 1/2, 1/2;
  0,  0,  1/6,  1/6;
  0,  0,  1/24, 1/24,  1/24;
  0,  0,   0,   1/120, 1/120,   1/120;
  0,  0,   0,   1/720, 1/720,   1/720,     1/720;
  0,  0,   0,    0,    1/5040,  1/5040,    1/5040,    1/5040;
  0,  0,   0,    0,    1/40320, 1/40320,   1/40320,   1/40320,   1/40320;
  0,  0,   0,    0,     0,      1/362880,  1/362880,  1/362880,  1/362880,  1/362880;
  0,  0,   0,    0,     0,      1/3628800, 1/3628800, 1/3628800, 1/3628800, 1/3628800, 1/3628800;