A275611 a(0) = 1, a(n) = n * a(n-1)^2 + a(n-1).
1, 2, 10, 310, 384710, 740009305210, 3285682630785061608169810, 75569972451698504356522006689642008796426176222510, 45686565890803766858880247710072390769807010129716258796255559717444312778982342222557219570421823310
Offset: 0
Links
- N. J. A. Sloane, A Nasty Surprise in a Sequence and Other OEIS Stories, Experimental Mathematics Seminar, Rutgers University, Oct 10 2024, Youtube video; Slides [Mentions this sequence]
Programs
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Mathematica
a[n_] := a[n - 1] (n*a[n - 1] + 1); a[0] = 1; Array[a, 9, 0] (* Robert G. Wilson v, Dec 24 2016 *)
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PARI
a(n) = if(n==0, 1, n * a(n-1)^2 + a(n-1));
Formula
a(n) ~ c^(2^n) / n, where c = 2.49513423157979814033214501746049499374370018515926861932281537537499551261588753466... - Vaclav Kotesovec, Jan 28 2019
a(n) = A295391(n)*a(n-1), n >= 1. - N. J. A. Sloane, Sep 03 2024