A291954 Triangle read by rows: T(n,k) = T(n-k,k-1) - T(n-k,k) with T(0,0) = 1 for 0 <= k <= A003056(n).

1, 0, 1, 0, -1, 0, 1, 1, 0, -1, -1, 0, 1, 0, 0, -1, 0, 1, 0, 1, 1, -1, 0, -1, -1, 0, 0, 1, 0, -1, 0, -1, 0, 2, 1, 0, 1, 1, -1, -1, 0, -1, -1, 1, 0, 0, 1, 0, -2, -1, 0, -1, 0, 2, 1, 0, 1, 1, -2, 0, 1, 0, -1, -1, 2, 1, -1, 0, 1, 0, -2, -1, 0, 0, -1, 0, 3, 1, -1, 0, 1

Offset

0,34

Links

Seiichi Manyama, Rows n = 0..481, flattened

Formula

G.f. of column k: x^(k*(k+1)/2) / Product_{j=1..k} (1+x^j).

Example

First few rows are:
  1;
  0,  1;
  0, -1;
  0,  1,  1;
  0, -1, -1;
  0,  1,  0;
  0, -1,  0,  1;
  0,  1,  1, -1;
  0, -1, -1,  0;
  0,  1,  0, -1;
  0, -1,  0,  2, 1.

Crossrefs

Row sums give A003406.

Columns 0-1 give A000007, A062157.

Cf. A008289, A291895, A291929.

Sequence in context: A037871 A037853 A255237 * A339885 A106799 A212210

Adjacent sequences: A291951 A291952 A291953 * A291955 A291956 A291957

Keyword

sign,tabf

Author

Seiichi Manyama, Sep 06 2017

Status

approved