Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #4 Nov 20 2017 22:00:24
%S 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,
%T 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,
%U 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
%N 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!).
%F E.g.f. of column k: exp(-Sum_{j=1..k} x^j/j!).
%e Square array begins:
%e 1, 1, 1, 1, 1, 1, ...
%e 0, -1 -1, -1, -1, -1, ...
%e 0, 1, 0, 0, 0, 0, ...
%e 0, -1, 2, 1, 1, 1, ...
%e 0, 1, -2, 2, 1, 1, ...
%e 0, -1, -6, -6, -1, -2, ...
%t 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
%t 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
%Y Columns k=0..3 give A000007, A033999, A001464, A014775.
%Y Main diagonal gives A000587.
%Y Cf. A229223.
%K sign,tabl
%O 0,19
%A _Ilya Gutkovskiy_, Nov 20 2017