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 A363005 #10 May 13 2023 13:49:40 %S A363005 1,1,2,4,12,56,416,4764,84272,2278740,92890636,5659487836 %N A363005 Number of sequences of n distinct integers whose Gilbreath transform is (1, 1, ..., 1). %C A363005 a(n) is even for all n >= 2, because if the sequence (x_1, ..., x_n) has Gilbreath transform (1, ..., 1), so has the sequence (2 - x_1, ..., 2 - x_n). %C A363005 Negative terms are permitted. %e A363005 For n = 4, the following 6 sequences, together with the sequences obtained by replacing each term x by 2-x in each of these sequences, have Gilbreath transform (1, 1, 1, 1), so a(4) = 12. %e A363005 (1, 2, 0, -4), %e A363005 (1, 2, 0, -2), %e A363005 (1, 2, 0, 4), %e A363005 (1, 2, 4, 0), %e A363005 (1, 2, 4, 6), %e A363005 (1, 2, 4, 8). %Y A363005 Cf. A080839 (increasing sequences), A363002 (nondecreasing sequences), A363003, A363004 (distinct positive integers). %K A363005 nonn,more %O A363005 0,3 %A A363005 _Pontus von Brömssen_, May 13 2023