A291678 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, -2, -2, 1, 0, 1, 6, 10, 0, -6, 2, 1, 0, 1, 7, 15, 5, -11, 0, 5, -1, 0, 1, 8, 21, 14, -15, -8, 12, 0, -2, 0, 1, 9, 28, 28, -15, -24, 18, 9, -8, 0, 0, 1, 10, 36, 48, -7, -48, 15, 32, -15, -6, 2

Offset

0,8

Links

Seiichi Manyama, Antidiagonals n = 0..139, flattened

Formula

G.f. of column k: Product_{j>=1} ((1 - x^(5*j-2))*(1 - x^(5*j-3)) / ((1 - x^(5*j-1))*(1 - x^(5*j-4))))^k.

Example

Square array begins:
   1,  1,  1,  1,   1, ...
   0,  1,  2,  3,   4, ...
   0,  0,  1,  3,   6, ...
   0, -1, -2, -2,   0, ...
   0,  0, -2, -6, -11, ...

Crossrefs

Columns k=0..4 give A000007, A003823, A285442, A285443, A285444.

Rows n=0..1 give A000012, A001477.

Main diagonal gives A291679.

Antidiagonal sums give A302016.

Cf. A286509.

Sequence in context: A275001 A290975 A367145 * A286180 A291701 A286352

Adjacent sequences: A291675 A291676 A291677 * A291679 A291680 A291681

Keyword

sign,tabl

Author

Seiichi Manyama, Aug 29 2017

Status

approved