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

1, 1, 2, 4, 12, 56, 416, 4764, 84272, 2278740, 92890636, 5659487836

Offset: 0

Author

Pontus von Brömssen, May 13 2023

Keywords

• nonn
• more

Comments

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).

Negative terms are permitted.

Examples

			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.
  (1, 2, 0, -4),
  (1, 2, 0, -2),
  (1, 2, 0,  4),
  (1, 2, 4,  0),
  (1, 2, 4,  6),
  (1, 2, 4,  8).
		

Crossrefs

Cf. A080839 (increasing sequences), A363002 (nondecreasing sequences), A363003, A363004 (distinct positive integers).