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A159830 Exponential Riordan array [exp(exp(x)-1-2x),x].

%I A159830 #7 Jul 22 2025 06:24:18
%S A159830 1,-1,1,2,-2,1,-3,6,-3,1,7,-12,12,-4,1,-10,35,-30,20,-5,1,31,-60,105,
%T A159830 -60,30,-6,1,-21,217,-210,245,-105,42,-7,1,204,-168,868,-560,490,-168,
%U A159830 56,-8,1,307,1836,-756,2604,-1260,882,-252,72,-9,1,2811,3070,9180,-2520,6510,-2520,1470,-360,90,-10,1
%N A159830 Exponential Riordan array [exp(exp(x)-1-2x),x].
%C A159830 First column is A126617. Row sums are A000296. A007318*A159830 is A124323.
%C A159830 The inverse is [exp(-exp(x)+1+2x),x] which has production matrix given by
%C A159830 1, 1,
%C A159830 -1, 1, 1,
%C A159830 -1, -2, 1, 1,
%C A159830 -1, -3, -3, 1, 1,
%C A159830 -1, -4, -6, -4, 1, 1 ...
%F A159830 G.f.: 1/(1-xy+x-x^2/(1-xy-2x^2/(1-xy-x-3x^2/(1-xy-2x-4x^2/(1-... (continued fraction).
%e A159830 Triangle begins
%e A159830 1,
%e A159830 -1, 1,
%e A159830 2, -2, 1,
%e A159830 -3, 6, -3, 1,
%e A159830 7, -12, 12, -4, 1,
%e A159830 -10, 35, -30, 20, -5, 1,
%e A159830 31, -60, 105, -60, 30, -6, 1,
%e A159830 -21, 217, -210, 245, -105, 42, -7, 1,
%e A159830 204, -168, 868, -560, 490, -168, 56, -8, 1
%e A159830 Production array is
%e A159830 -1, 1,
%e A159830 1, -1, 1,
%e A159830 1, 2, -1, 1,
%e A159830 1, 3, 3, -1, 1,
%e A159830 1, 4, 6, 4, -1, 1,
%e A159830 1, 5, 10, 10, 5, -1, 1,
%e A159830 1, 6, 15, 20, 15, 6, -1, 1,
%e A159830 1, 7, 21, 35, 35, 21, 7, -1, 1,
%e A159830 1, 8, 28, 56, 70, 56, 28, 8, -1, 1
%t A159830 (* The function RiordanArray is defined in A256893. *)
%t A159830 RiordanArray[Exp[Exp[#] - 1 - 2 #]&, #&, 11, True] // Flatten (* _Jean-François Alcover_, Jul 19 2019 *)
%K A159830 easy,sign,tabl
%O A159830 0,4
%A A159830 _Paul Barry_, Apr 23 2009