OFFSET
0,3
COMMENTS
Also, numbers remaining after the following sieving process: In step 1, keep all numbers of the set N={0,1,2,...}. In step 2, keep only every second number after a(2)=2: N'={0,1,2,4,6,8,10,...}. In step 3, keep every 4th of the numbers following a(3)=4, N"={0,1,2,4,12,20,28,...}. In step 4, keep every 12th of the numbers beyond a(4)=12: {0,1,2,4,12,108,204,...}. In step 5, keep every 108th of the numbers beyond a(5)=108: {0,1,2,4,12,108,10476,...}, and so on. The next "gap" a(n+1)-a(n) is always a(n) times the former gap, i.e., a(n+1)-a(n) = a(n)*(a(n)-a(n-1)). - M. F. Hasler, Oct 28 2010
Number of plane trees where the root has fewer than n children and the i-th child of any node has fewer than i children. - David Eppstein, Dec 18 2021
REFERENCES
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
John Cerkan, Table of n, a(n) for n = 0..13
A. V. Aho and N. J. A. Sloane, Some doubly exponential sequences, Fibonacci Quarterly, Vol. 11, No. 4 (1973), pp. 429-437.
A. V. Aho and N. J. A. Sloane, Some doubly exponential sequences, Fibonacci Quarterly, Vol. 11, No. 4 (1973), pp. 429-437 (original plus references that F.Q. forgot to include - see last page!)
FORMULA
a(n) ~ c^(2^n), where c = 1.15552822483840350150537253088299651035583896919522349372370013726451673646... . - Vaclav Kotesovec, May 21 2015
MATHEMATICA
a[0] = 0; a[1] = 1; a[n_] := a[n] = a[n-1]*(1 + a[n-1] - a[n-2]); Table[a[n], {n, 0, 10}] (* Jean-François Alcover, Jul 02 2013 *)
PROG
(PARI) a(n)=if(n<2, n>0, a(n-1)*(1+a(n-1)-a(n-2)))
(Haskell)
a001696 n = a001696_list !! n
a001696_list = 0 : 1 : zipWith (-)
(zipWith (+) a001696_list' $ map (^ 2) a001696_list')
(zipWith (*) a001696_list a001696_list')
where a001696_list' = tail a001696_list
-- Reinhard Zumkeller, Apr 29 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved