%I #9 May 13 2023 13:48:09
%S 1,1,2,6,26,166,1562,21614,438594,13032614,566069882
%N Number of integer sequences of length n whose Gilbreath transform is (1, 1, ..., 1).
%C 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 Negative terms are permitted.
%e For n = 4, the following 13 sequences, together with the sequences obtained by replacing each term x by 2x in each of these sequences, have Gilbreath transform (1, 1, 1, 1), so a(4) = 26.
%e (1, 2, 0, 4),
%e (1, 2, 0, 2),
%e (1, 2, 0, 0),
%e (1, 2, 0, 2),
%e (1, 2, 0, 4),
%e (1, 2, 2, 0),
%e (1, 2, 2, 2),
%e (1, 2, 2, 4),
%e (1, 2, 4, 0),
%e (1, 2, 4, 2),
%e (1, 2, 4, 4),
%e (1, 2, 4, 6),
%e (1, 2, 4, 8).
%Y Cf. A080839 (increasing sequences), A363002 (nondecreasing sequences), A363004 (distinct positive integers), A363005 (distinct integers).
%K nonn,more
%O 0,3
%A _Pontus von BrÃ¶mssen_, May 13 2023
