

A080839


Number of positive increasing integer sequences of length n with Gilbreath transform (that is, the diagonal of leading successive absolute differences) given by {1,1,1,1,1,...}.


4



1, 1, 1, 2, 6, 27, 180, 1786, 26094, 559127, 17535396, 804131875, 53833201737
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OFFSET

1,4


COMMENTS

The slowestgrowing sequence of length n is 1,2,4,6,...,2(n1). The fastestgrowing sequence is 1,2,4,8,...,2^(n1).
The ratio a(n+1)a(n1)/a(n)^2 appears to converge to a constant near 1.46, which is the approximate growth rate of A001609. Are the sequences related?
(End)
Also, a(n) is the number of (not necessarily increasing) positive integer sequences of length n1 with Gilbreath transform (1, ..., 1).  Pontus von Brömssen, May 13 2023


LINKS



EXAMPLE

The table below shows that {1,2,4,6,10} is one of the 6 sequences of length 5 that satisfy the stated condition:
1
2 1
4 2 1
6 2 0 1
10 4 2 2 1


CROSSREFS



KEYWORD

nonn,more


AUTHOR



EXTENSIONS



STATUS

approved



