cp's OEIS Frontend

A382437 a(n) = a(n-1)^2 + 4 * a(n-1), with a(0) = 2.

%I A382437 #25 Apr 06 2025 22:18:05
%S A382437 2,12,192,37632,1416317952,2005956546822746112,
%T A382437 4023861667741036022825635656102100992,
%U A382437 16191462721115671781777559070120513664958590125499158514329308740975788032
%N A382437 a(n) = a(n-1)^2 + 4 * a(n-1), with a(0) = 2.
%H A382437 Paolo Xausa, <a href="/A382437/b382437.txt">Table of n, a(n) for n = 0..10</a>
%F A382437 a(n) = A003010(n) - 2.
%F A382437 a(n)/2 = A002812(n) - 1.
%F A382437 For n > 1: a(n) = 3 * 2^(2*n) * Product_{i = 0..n-2} A002812(i)^2.
%F A382437 Conjecture: a(n) = Sum_{k=1..2^n} (2^n * 2^k * binomial(2^n + k - 1, 2*k - 1) / k).
%t A382437 NestList[#*(4 + #) &, 2, 8] (* _Paolo Xausa_, Apr 01 2025 *)
%o A382437 (PARI) a(n)=if(n, a(n-1)^2 + 4*a(n-1), 2);
%o A382437 vector(8, i, a(i-1))
%Y A382437 Cf. A002812, A003010.
%K A382437 nonn
%O A382437 0,1
%A A382437 _V. Barbera_, Mar 25 2025