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%I #10 May 13 2023 13:49:40
%S 1,1,2,4,12,56,416,4764,84272,2278740,92890636,5659487836
%N Number of sequences of n distinct integers 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 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 (1, 2, 0, -4),
%e (1, 2, 0, -2),
%e (1, 2, 0, 4),
%e (1, 2, 4, 0),
%e (1, 2, 4, 6),
%e (1, 2, 4, 8).
%Y Cf. A080839 (increasing sequences), A363002 (nondecreasing sequences), A363003, A363004 (distinct positive integers).
%K nonn,more
%O 0,3
%A _Pontus von Brömssen_, May 13 2023
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