A127767 Inverse of number triangle A(n,k) = 1/C(n) if k <= n <= 2k, 0 otherwise, where C(n) = A000108(n).

1, 0, 1, 0, -1, 2, 0, 1, -2, 5, 0, 0, 0, -5, 14, 0, -1, 2, 0, -14, 42, 0, 0, 0, 0, 0, -42, 132, 0, 1, -2, 5, 0, 0, -132, 429, 0, 0, 0, 0, 0, 0, 0, -429, 1430, 0, 0, 0, -5, 14, 0, 0, 0, -1430, 4862, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4862, 16796

Offset

0,6

Comments

It is conjectured that all elements of the triangle are integers.

Links

Table of n, a(n) for n=0..65.

Example

Triangle begins
  1;
  0,  1;
  0, -1,  2;
  0,  1, -2,  5;
  0,  0,  0, -5,  14;
  0, -1,  2,  0, -14,  42;
  0,  0,  0,  0,   0, -42,  132;
  0,  1, -2,  5,   0,   0, -132,  429;
  0,  0,  0,  0,   0,   0,    0, -429,  1430;
  0,  0,  0, -5,  14,   0,    0,    0, -1430,  4862;
  0,  0,  0,  0,   0,   0,    0,    0,     0, -4862, 16796;
Inverse of triangle begins
  1;
  0,  1;
  0, 1/2, 1/2;
  0,  0,  1/5,  1/5;
  0,  0,  1/14, 1/14,  1/14;
  0,  0,   0,   1/42,  1/42,   1/42;
  0,  0,   0,   1/132, 1/132,  1/132,   1/132;
  0,  0,   0,    0,    1/429,  1/429,   1/429,   1/429;
  0,  0,   0,    0,    1/1430, 1/1430,  1/1430,  1/1430,  1/1430;
  0,  0,   0,    0,     0,     1/4862,  1/4862,  1/4862,  1/4862,  1/4862;
  0,  0,   0,    0,     0,     1/16796, 1/16796, 1/16796, 1/16796, 1/16796, 1/16796;

Prog

(PARI) row(n) = {n++; my(m = matrix(n, n, i, j, i--; j--; if ((i >= j) && (i <= 2*j), (i+1)/binomial(2*i, i), 0))); m = m^(-1); m[n, ]; } \\ Michel Marcus, Sep 30 2018

Crossrefs

Cf. A000108.

Row sums give A127768.

Sequence in context: A074704 A025247 A341439 * A292577 A055509 A334226

Adjacent sequences: A127764 A127765 A127766 * A127768 A127769 A127770

Keyword

sign,tabl

Author

Paul Barry, Jan 28 2007

Status

approved