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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!).
0
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
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
KEYWORD
sign,tabl
AUTHOR
Ilya Gutkovskiy, Nov 20 2017
STATUS
approved