A295343 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f. exp(-Sum_{j=1..k} x^j/j!).

1, 1, 0, 1, -1, 0, 1, -1, 1, 0, 1, -1, 0, -1, 0, 1, -1, 0, 2, 1, 0, 1, -1, 0, 1, -2, -1, 0, 1, -1, 0, 1, 2, -6, 1, 0, 1, -1, 0, 1, 1, -6, 16, -1, 0, 1, -1, 0, 1, 1, -1, -14, 20, 1, 0, 1, -1, 0, 1, 1, -2, -14, 20, -132, -1, 0, 1, -1, 0, 1, 1, -2, -8, -15, 204, -28, 1, 0, 1, -1, 0, 1, 1, -2, -9, -15, 99, 28, 1216, -1, 0

Offset

0,19

Links

Table of n, a(n) for n=0..90.

Formula

E.g.f. of column k: exp(-Sum_{j=1..k} x^j/j!).

Example

Square array begins:
1,  1,  1,  1,  1,  1,  ...
0, -1  -1, -1, -1, -1,  ...
0,  1,  0,  0,  0,  0,  ...
0, -1,  2,  1,  1,  1,  ...
0,  1, -2,  2,  1,  1,  ...
0, -1, -6, -6, -1, -2,  ...

Mathematica

Table[Function[k, n! SeriesCoefficient[Exp[-Sum[x^i/i!, {i, 1, k}]], {x, 0, n}]][j - n], {j, 0, 12}, {n, 0, j}] // Flatten
Table[Function[k, n! SeriesCoefficient[Exp[1 - Exp[x] Gamma[k + 1, x]/Gamma[k + 1]], {x, 0, n}]][j - n], {j, 0, 12}, {n, 0, j}] // Flatten

Crossrefs

Columns k=0..3 give A000007, A033999, A001464, A014775.

Main diagonal gives A000587.

Cf. A229223.

Sequence in context: A070107 A299908 A044933 * A025915 A081285 A255361

Adjacent sequences: A295340 A295341 A295342 * A295344 A295345 A295346

Keyword

sign,tabl

Author

Ilya Gutkovskiy, Nov 20 2017

Status

approved