A293134 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f. exp(-x^(k+1)/(1+x)).

1, 1, -1, 1, 0, 3, 1, 0, -2, -13, 1, 0, 0, 6, 73, 1, 0, 0, -6, -12, -501, 1, 0, 0, 0, 24, 0, 4051, 1, 0, 0, 0, -24, -120, 240, -37633, 1, 0, 0, 0, 0, 120, 1080, -2520, 394353, 1, 0, 0, 0, 0, -120, -720, -10080, 21840, -4596553, 1, 0, 0, 0, 0, 0, 720, 5040, 100800

Offset

0,6

Links

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

Formula

A(0,k) = 1, A(1,k) = A(2,k) = ... = A(k,k) = 0 and A(n,k) = (-1)^(k+1) * Sum_{i=k..n-1} (-1)^i*(i+1)!*binomial(n-1,i)*A(n-1-i,k) for n > k.

Example

Square array begins:
      1,   1,    1,   1, ...
     -1,   0,    0,   0, ...
      3,  -2,    0,   0, ...
    -13,   6,   -6,   0, ...
     73, -12,   24, -24, ...
   -501,   0, -120, 120, ...

Crossrefs

Columns k=0..2 give A293125, A293122, A293123.

Rows n=0..1 give A000012, (-1)*A000007.

Main diagonal gives A000007.

A(n,n-1) gives (-1)*A000142(n).

Cf. A293053, A293119, A293133.

Sequence in context: A357438 A324173 A355666 * A293053 A355652 A355665

Adjacent sequences: A293131 A293132 A293133 * A293135 A293136 A293137

Keyword

sign,tabl

Author

Seiichi Manyama, Sep 30 2017

Status

approved