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%I #35 Oct 20 2024 23:45:55
%S 1,2,10,310,384710,740009305210,3285682630785061608169810,
%T 75569972451698504356522006689642008796426176222510,
%U 45686565890803766858880247710072390769807010129716258796255559717444312778982342222557219570421823310
%N a(0) = 1, a(n) = n * a(n-1)^2 + a(n-1).
%H N. J. A. Sloane, <a href="https://www.youtube.com/watch?v=3RAYoaKMckM">A Nasty Surprise in a Sequence and Other OEIS Stories</a>, Experimental Mathematics Seminar, Rutgers University, Oct 10 2024, Youtube video; <a href="https://sites.math.rutgers.edu/~zeilberg/expmath/sloane85BD.pdf">Slides</a> [Mentions this sequence]
%F a(n) ~ c^(2^n) / n, where c = 2.49513423157979814033214501746049499374370018515926861932281537537499551261588753466... - _Vaclav Kotesovec_, Jan 28 2019
%F a(n) = A295391(n)*a(n-1), n >= 1. - _N. J. A. Sloane_, Sep 03 2024
%t a[n_] := a[n - 1] (n*a[n - 1] + 1); a[0] = 1; Array[a, 9, 0] (* _Robert G. Wilson v_, Dec 24 2016 *)
%o (PARI) a(n) = if(n==0, 1, n * a(n-1)^2 + a(n-1));
%Y Cf. A052129, A295391.
%K nonn,easy
%O 0,2
%A _Daniel Suteu_, Dec 24 2016