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

[Antti Karttunen]

Joshua Zucker wrote:

> 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.
>
Table http://www.research.att.com/~njas/sequences/A080934 ???

-- Antti

> Thanks,
> --Joshua Zucker
>