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

2, 12, 192, 37632, 1416317952, 2005956546822746112, 4023861667741036022825635656102100992, 16191462721115671781777559070120513664958590125499158514329308740975788032

Offset: 0

Author

V. Barbera, Mar 25 2025

Keywords

• nonn

Links

• Paolo Xausa, Table of n, a(n) for n = 0..10

Crossrefs

Cf. A002812, A003010.

Programs

Mathematica

NestList[#*(4 + #) &, 2, 8] (* Paolo Xausa, Apr 01 2025 *)

PARI

a(n)=if(n, a(n-1)^2 + 4*a(n-1), 2);
vector(8, i, a(i-1))

Formula

a(n) = A003010(n) - 2.

a(n)/2 = A002812(n) - 1.

For n > 1: a(n) = 3 * 2^(2*n) * Product_{i = 0..n-2} A002812(i)^2.

Conjecture: a(n) = Sum_{k=1..2^n} (2^n * 2^k * binomial(2^n + k - 1, 2*k - 1) / k).