%I #13 Sep 18 2024 08:01:33
%S 0,1,3,9,36,117,411,1452,5040,17829,62870,222458,789895,2808018,
%T 10006020,35713288,127657287,456975112,1637845137,5876993799,
%U 21110257429,75900966585,273140226328,983733709424,3545658087397,12788512426396,46155740640489,166684398100813,602296651467057,2177492178467267,7876245417001355
%N Number of nondecreasing arrangements of n numbers x(i) in -(n-1)..(n-1) with the sum of sign(x(i))*2^|x(i)| zero.
%e All solutions for n=3:
%e .-1...-2...-1
%e .-1....1....0
%e ..2....1....0
%t AatE[n_, nminusfE_, E_] := AatE[n, nminusfE, E] = Module[{a, fEminus, fEplus, f0, resn}, If[E == 0, If[n == 0, 1, 0], a = 0; For[fEminus = 0, fEminus <= nminusfE, fEminus++, For[fEplus = 0, fEplus <= nminusfE - fEminus, fEplus++, f0 = nminusfE - fEminus - fEplus; resn = n - (2^E + 1)*fEminus + (2^E - 1)*fEplus; If[Abs[resn] <= (1 + 2^(E - 1))*f0, a = a + AatE[resn, f0, E - 1]]]]; a]];
%t T[n_, k_] := AatE[n, n, n + k - 2];
%t Table[T[n, 1], {n, 1, 31}] (* _Jean-François Alcover_, Sep 18 2024, after _R. J. Mathar_ in A187988 *)
%Y Column 1 of A187988.
%K nonn
%O 1,3
%A _R. H. Hardin_, Mar 18 2011
%E More terms from _R. J. Mathar_, May 11 2023