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 A363003 #9 May 13 2023 13:48:09 %S A363003 1,1,2,6,26,166,1562,21614,438594,13032614,566069882 %N A363003 Number of integer sequences of length n whose Gilbreath transform is (1, 1, ..., 1). %C A363003 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 A363003 Negative terms are permitted. %e A363003 For n = 4, the following 13 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) = 26. %e A363003 (1, 2, 0, -4), %e A363003 (1, 2, 0, -2), %e A363003 (1, 2, 0, 0), %e A363003 (1, 2, 0, 2), %e A363003 (1, 2, 0, 4), %e A363003 (1, 2, 2, 0), %e A363003 (1, 2, 2, 2), %e A363003 (1, 2, 2, 4), %e A363003 (1, 2, 4, 0), %e A363003 (1, 2, 4, 2), %e A363003 (1, 2, 4, 4), %e A363003 (1, 2, 4, 6), %e A363003 (1, 2, 4, 8). %Y A363003 Cf. A080839 (increasing sequences), A363002 (nondecreasing sequences), A363004 (distinct positive integers), A363005 (distinct integers). %K A363003 nonn,more %O A363003 0,3 %A A363003 _Pontus von Brömssen_, May 13 2023