A291701 Square array A(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of k-th power of continued fraction 1 - x/(1 - x^2/(1 - x^3/(1 - x^4/(1 - x^5/(1 - ...))))).

1, 1, 0, 1, -1, 0, 1, -2, 0, 0, 1, -3, 1, -1, 0, 1, -4, 3, -2, 0, 0, 1, -5, 6, -4, 2, -1, 0, 1, -6, 10, -8, 6, -2, -1, 0, 1, -7, 15, -15, 13, -6, 1, -1, 0, 1, -8, 21, -26, 25, -16, 6, 0, -2, 0, 1, -9, 28, -42, 45, -36, 18, -3, 0, -2, 0, 1, -10, 36, -64, 77, -72

Offset: 0

Author

Seiichi Manyama, Aug 30 2017

Keywords

• sign
• tabl

Examples

			Square array begins:
   1,  1,  1,  1,  1, ...
   0, -1, -2, -3, -4, ...
   0,  0,  1,  3,  6, ...
   0, -1, -2, -4, -8, ...
   0,  0,  2,  6, 13, ...
		

Crossrefs

Columns k=0..1 give A000007, A291148.

Rows n=0..1 give A000012, A001489.

Main diagonal gives A291702.

Cf. A291652.

Formula

G.f. of column k: (1 - x/(1 - x^2/(1 - x^3/(1 - x^4/(1 - x^5/(1 - ...))))))^k, a continued fraction.