%I M1301 N0499 #34 Feb 02 2022 23:47:38
%S 1,2,4,24,1104,2435424,11862575248704,281441383062305809756861824,
%T 158418504200047111075388369241884118003210485743490304
%N From a slowly converging series.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A. V. Aho and N. J. A. Sloane, <a href="https://www.fq.math.ca/Scanned/11-4/aho-a.pdf">Some doubly exponential sequences</a>, Fibonacci Quarterly, Vol. 11, No. 4 (1973), pp. 429-437, <a href="http://neilsloane.com/doc/doubly.html">alternative link</a>.
%H H. E. Salzer, <a href="http://www.jstor.org/stable/2305906">The approximation of numbers as sums of reciprocals</a>, Amer. Math. Monthly, Vol. 54, No. 3 (1947), pp. 135-142.
%H <a href="/index/Aa#AHSL">Index entries for sequences of form a(n+1)=a(n)^2 + ...</a>
%F Apparently a(n+2) = A002715(2*n) + 1. - _R. J. Mathar_, Apr 23 2007
%F From _Amiram Eldar_, Feb 02 2022: (Start)
%F a(n) = 2*a(n-1)*(a(n-1)-1) for n > 1.
%F a(n) = floor(1 + phi^(2^n)/2), where phi is the golden ratio (A001622) (Aho and Sloane, 1973). (End)
%t (* a5 = A002715 *) a5[n_?OddQ] := a5[n] = 2*a5[n-1] + 1; a5[n_?EvenQ] := a5[n] = (a5[n-1]^2 - 3)/2; a5[0] = 3; a[n_] := a5[2*n - 4] + 1; a[0] = 1; a[1] = 2; Table[a[n], {n, 0, 8}] (* _Jean-François Alcover_, Jan 25 2013, after _R. J. Mathar_ *)
%t Join[{1}, RecurrenceTable[{a[1] == 2, a[n] == 2*a[n - 1]*(a[n - 1] - 1)}, a, {n, 1, 8}]] (* _Amiram Eldar_, Feb 02 2022 *)
%Y Cf. A001622, A002715.
%K nonn,nice
%O 0,2
%A _N. J. A. Sloane_