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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.

A363005 Number of sequences of n distinct integers whose Gilbreath transform is (1, 1, ..., 1).

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%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