[SeqFan]: Repeated iterations of INVERT starting from A019590 ?

[Joshua Zucker]

Oh, one more comment:
if I start with the empty seq
A000004 (0,0,0,0...)
and prepend 1 and invert repeatedly, I get
A000012 all 1s
A000079 powers of 2
A001519 bisection of Fibonacci
A007051 (3^n + 1)/2
A080937 (which is a "restricted Catalan" of maximum 5)
A024175 (which might also be related to Catalan in the same way as
A080937 and A080938, unless there's something really different about
odd and even numbers here?)
A080938 (which is a "restricted Catalan" of maximum 7)
A033191 (related to binomial transform of Fibonacci - but isn't
binomial of fibonacci related to fibonacci itself in a pretty direct
way?)
And finally a seq not yet in OEIS:
1 2 5 14 42 132 429 1430 4862 16795 58766 207783 740924 2660139
9603089 34818270 126676726 462125928 1689438278 6186432967 22682699779
83249302471 305773834030 1123771473120 4131947428007 15197952958467
55915691993228 205765906819451 757326699164035 2787706774345669
10262482704258873 37782416217093813 139107832756053214
512191460458891717 1885938860769281490 6944389239984279502

Someone (Antti?) might want to submit the relevant comments.

Thanks,
--Joshua Zucker