This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A104556 #30 Mar 27 2020 06:58:10
%S A104556 1,-1,1,0,-3,1,0,3,-6,1,0,0,15,-10,1,0,0,-15,45,-15,1,0,0,0,-105,105,
%T A104556 -21,1,0,0,0,105,-420,210,-28,1,0,0,0,0,945,-1260,378,-36,1,0,0,0,0,
%U A104556 -945,4725,-3150,630,-45,1,0,0,0,0,0,-10395,17325,-6930,990,-55,1,0,0,0,0,0,10395,-62370,51975,-13860,1485,-66,1
%N A104556 Matrix inverse of triangle A001497 of Bessel polynomials, read by rows; essentially the same as triangle A096713 of modified Hermite polynomials.
%C A104556 Exponential Riordan array [1 - x, x - x^2/2]; cf. A049403. - _Peter Bala_, Apr 08 2013
%C A104556 Also the Bell transform of (-1)^n if n<2 else 0 and the inverse Bell transform of A001147(n) (adding 1,0,0,... as column 0). For the definition of the Bell transform see A264428. - _Peter Luschny_, Jan 19 2016
%H A104556 G. C. Greubel, <a href="/A104556/b104556.txt">Rows n=0..35 of triangle, flattened</a>
%H A104556 H. Han and S. Seo, <a href="http://dx.doi.org/10.1016/j.ejc.2007.12.002">Combinatorial proofs of inverse relations and log-concavity for Bessel numbers</a>, Eur. J. Combinat. 29 (7) (2008) 1544-1554. [From _R. J. Mathar_, Mar 20 2009]
%F A104556 E.g.f. : (1 - t)*exp(x*(t - t^2/2)) = 1 + (-1 + x)*t + (-3*x + x^2)*t^2/2! + ... - _Peter Bala_, Apr 08 2013
%e A104556 Rows begin:
%e A104556 1;
%e A104556 -1, 1;
%e A104556 0, -3, 1;
%e A104556 0, 3, -6, 1;
%e A104556 0, 0, 15, -10, 1;
%e A104556 0, 0, -15, 45, -15, 1;
%e A104556 0, 0, 0, -105, 105, -21, 1;
%e A104556 0, 0, 0, 105, -420, 210, -28, 1;
%e A104556 0, 0, 0, 0, 945, -1260, 378, -36, 1;
%e A104556 0, 0, 0, 0, -945, 4725, -3150, 630, -45, 1; ...
%e A104556 The columns being equal in absolute value to the rows of the matrix inverse A001497:
%e A104556 1;
%e A104556 1, 1;
%e A104556 3, 3, 1;
%e A104556 15, 15, 6, 1;
%e A104556 105, 105, 45, 10, 1;
%e A104556 945, 945, 420, 105, 15, 1; ...
%t A104556 With[{nmax = 10}, CoefficientList[CoefficientList[Series[(1 - t)*Exp[x*(t - t^2/2)], {t, 0, nmax}, {x, 0, nmax}], t], x]*Range[0, nmax]!] (* _G. C. Greubel_, Jun 10 2018 *)
%o A104556 (Sage) # uses[bell_matrix from A264428]
%o A104556 # Adds a column 1,0,0,0, ... at the left side of the triangle.
%o A104556 bell_matrix(lambda n: (-1)^n if n<2 else 0, 9) # _Peter Luschny_, Jan 19 2016
%Y A104556 Row sums are found in A001464 (offset 1).
%Y A104556 Absolute row sums equal A000085.
%Y A104556 Cf. A001497, A049403, A096713, A122848, A130757.
%K A104556 sign,tabl
%O A104556 0,5
%A A104556 _Paul D. Hanna_, Mar 14 2005