A038498 Matrix inverse of partition triangle A008284.

1, -1, 1, 0, -1, 1, 1, -1, -1, 1, 0, 1, -1, -1, 1, 0, 1, 0, -1, -1, 1, -1, 1, 1, 0, -1, -1, 1, -1, 0, 2, 0, 0, -1, -1, 1, 0, -1, 0, 2, 0, 0, -1, -1, 1, 0, -2, 1, 1, 1, 0, 0, -1, -1, 1, 1, -2, -1, 1, 1, 1, 0, 0, -1, -1, 1, 1, -1, -2, 0, 2, 0, 1, 0, 0, -1, -1, 1

Offset: 1

Author

Christian G. Bower, Feb 15 1999

Keywords

• sign
• tabl

Comments

Since A008284 has only ones in its first column, the sum of terms for any row n > 1 is 0. - François Marques, Feb 09 2021

Examples

			Triangle begins:
  1;
  -1,1;
  0,-1,1;
  1,-1,-1,1;
  ...
		

Crossrefs

Cf. A008284, A038497, A039800-A039810, A010815.

Programs

PARI

tp(n, k) = if (n<1, 0, if (k<1, 0, if (k == n, 1, if (k > n, 0, tp(n-1, k-1) + tp(n-k, k)))));
tabl(nn) = {mtp = matrix(nn, nn, n, k, tp(n, k)); mtpi = mtp^(-1); for (n = 1, nn, for (k = 1, n, print1(mtpi[n, k], ", ");); print(););} \\ Michel Marcus, Mar 04 2014

Formula

T(n,n-k) = A010815(k) for k <= n/2. - François Marques, Feb 09 2021