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 A161556 #17 Nov 03 2019 01:41:28
%S A161556 1,0,1,1,0,1,0,3,0,1,2,0,6,0,1,0,10,0,10,0,1,6,0,30,0,15,0,1,0,42,0,
%T A161556 70,0,21,0,1,24,0,168,0,140,0,28,0,1,0,216,0,504,0,252,0,36,0,1,120,0,
%U A161556 1080,0,1260,0,420,0,45,0,1
%N A161556 Exponential Riordan array [1 + (sqrt(Pi)/2)*x*exp(x^2/4)*erf(x/2), x].
%C A161556 Row sums are A084261.
%H A161556 G. C. Greubel, <a href="/A161556/b161556.txt">Table of n, a(n) for the first 50 rows, flattened</a>
%F A161556 T(n,k) = [k<=n]*binomial(n,k)*((n-k)/2)!*(1+(-1)^(n-k))/2.
%F A161556 G.f.: 1/(1-x*y-x^2/(1-x*y-x^2/(1-x*y-2x^2/(1-x*y-2x^2/(1-x*y-3x^2/(1-... (continued fraction).
%e A161556 Triangle begins
%e A161556 1;
%e A161556 0, 1;
%e A161556 1, 0, 1;
%e A161556 0, 3, 0, 1;
%e A161556 2, 0, 6, 0, 1;
%e A161556 0, 10, 0, 10, 0, 1;
%e A161556 6, 0, 30, 0, 15, 0, 1;
%e A161556 0, 42, 0, 70, 0, 21, 0, 1;
%e A161556 24, 0, 168, 0, 140, 0, 28, 0, 1;
%e A161556 Production matrix begins
%e A161556 0, 1;
%e A161556 1, 0, 1;
%e A161556 0, 2, 0, 1;
%e A161556 -1, 0, 3, 0, 1;
%e A161556 0, -4, 0, 4, 0, 1;
%e A161556 6, 0, -10, 0, 5, 0, 1;
%e A161556 0, 36, 0, -20, 0, 6, 0, 1;
%t A161556 T[n_, k_] := Boole[k <= n] Binomial[n, k] ((n-k)/2)! (1 + (-1)^(n-k))/2; Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, Sep 30 2016 *)
%Y A161556 Cf. A155856, A156367.
%K A161556 easy,nonn,tabl
%O A161556 0,8
%A A161556 _Paul Barry_, Jun 13 2009