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.
(4,1,3,5,2) has difference (3,-1,0,1,-3) and signs (1,-1,0,1,-1) with total 0.
b:= proc(s, t) option remember; (n-> `if`(abs(t)>n, 0, `if`(n=0, 1,
add(b(s minus {j}, t+signum(n-j)), j=s))))(nops(s))
end:
a:= n-> b({$1..n}, 0):
seq(a(n), n=0..14); # Alois P. Heinz, Jul 31 2018
E1[n_ /; n >= 0, 0] = 1;
E1[n_, k_] /; k < 0 || k > n = 0;
E1[n_, k_] := E1[n, k] = (n-k) E1[n-1, k-1] + (k+1) E1[n-1, k];
b[n_] := Sum[(-1)^(n-k) E1[n+k, n] Binomial[2n, n-k], {k, 0, n}];
a[n_] := Sum[Binomial[n, n-2k] b[k], {k, 0, n/2}];
a /@ Range[0, 150] (* Jean-François Alcover, Oct 29 2020, after Peter Luschny in A320337 *)
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