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A376768 a(1) = 2; thereafter, a(n) = c*A376767(n-1) + 1, where c=4 if n is even, c=2 if n is odd.

%I A376768 #14 Dec 16 2024 08:47:00
%S A376768 2,5,11,221,24311,1182000821,698562969831336611,
%T A376768 975980445639153806859347417915257421,
%U A376768 476268915135000629546288739757931900755190480621127468115605921390156911
%N A376768 a(1) = 2; thereafter, a(n) = c*A376767(n-1) + 1, where c=4 if n is even, c=2 if n is odd.
%C A376768 This is the sequence of dampening coefficients for the divergent series 1 + 2 + 1 + 2 + 1 + 2 + ...
%H A376768 Paolo Xausa, <a href="/A376768/b376768.txt">Table of n, a(n) for n = 1..12</a>
%H A376768 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>
%t A376768 A376767[n_] := A376767[n] = If[n == 1, 1, If[OddQ[n], 2, 4]*#^2 + # & [A376767[n-1]]];
%t A376768 A376768[n_] := If[n == 1, 2, If[OddQ[n], 2, 4]*A376767[n-1] + 1];
%t A376768 Array[A376768, 10] (* _Paolo Xausa_, Dec 16 2024 *)
%Y A376768 Cf. A374663, A376767.
%K A376768 nonn
%O A376768 1,1
%A A376768 _N. J. A. Sloane_, Nov 03 2024
%E A376768 Definition corrected by _N. J. A. Sloane_, Dec 15 2024 - thanks to _Paolo Xausa_ for noticing the error.