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