A334568 Square array A(n,k), n >= 0, k >= 1, read by antidiagonals downwards, where column k is the expansion of e.g.f. exp(-Sum_{j=1..k} x^j/j).

1, 1, -1, 1, -1, 1, 1, -1, 0, -1, 1, -1, 0, 2, 1, 1, -1, 0, 0, -2, -1, 1, -1, 0, 0, 6, -6, 1, 1, -1, 0, 0, 0, -6, 16, -1, 1, -1, 0, 0, 0, 24, -24, 20, 1, 1, -1, 0, 0, 0, 0, -24, -120, -132, -1, 1, -1, 0, 0, 0, 0, 120, -120, 540, -28, 1, 1, -1, 0, 0, 0, 0, 0, -120, -720, 1764, 1216, -1

Offset

0,14

Links

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

Formula

A(0,k) = 1 and A(n,k) = - (n-1)! * Sum_{j=1..min(k,n)} A(n-j,k)/(n-j)!.

Example

Square array begins:
   1,    1,    1,    1,    1,    1,    1, ...
  -1,   -1,   -1,   -1,   -1,   -1,   -1, ...
   1,    0,    0,    0,    0,    0,    0, ...
  -1,    2,    0,    0,    0,    0,    0, ...
   1,   -2,    6,    0,    0,    0,    0, ...
  -1,   -6,   -6,   24,    0,    0,    0, ...
   1,   16,  -24,  -24,  120,    0,    0, ...
  -1,   20, -120, -120, -120,  720,    0, ...
   1, -132,  540, -720, -720, -720, 5040, ...

Crossrefs

Columns k=1..5 give A033999, A001464, A334569, A334570, A334571.

Cf. A330858, A334561.

Sequence in context: A030351 A257994 A188921 * A072617 A348541 A210825

Adjacent sequences: A334565 A334566 A334567 * A334569 A334570 A334571

Keyword

sign,tabl

Author

Seiichi Manyama, May 06 2020

Status

approved