%I #6 Jun 20 2016 05:14:06

%S 2,5,38,2707,21418388,3000279372337641,

%T 255122481276683701099886061668842

%N Main diagonal of "square and add k" array.

%C Array of recurrence "start with 2, square and add k" begins:

%C k..|.A[k,n]=A[k,n-1]^2 + k

%C -1.|.2..3...8....63.......3968..15745023.247905749270528.............A003096

%C 0..|.2..4..16...256......65536..4294967296.18446744073709551616......A001146

%C 1..|.2..5..26...677.....458330..210066388901.44127887745906175987802.A003095

%C 2..|.2..6..38..1446....2090918.4371938082726...19113842599189892819591078...

%C 3..|.2..7..52..2707....7327852.53697414933907..2883412370584178505178284652.

%C 4..|.2..8..68..4628...21418388.458747344518548.210449126102819371741916028308.

%C 5..|.2..9..86..7401...54774806.3000279372337641.9001676312074749038996905444886.

%C 6..|.2.10.106.11242..126382570.1597255405035792810...

%C 7..|.2.11.128.16391..268664888.72180822044052551...

%C 8..|.2.12.152.23112..534164552.285331768613360712..

%C 9..|.2.13.178.31693.1004446258.1008912285210202573.

%C 10.|.2.14.206.42446.1801662926.3245989298922881486.

%F a(n) = A[n,n] where A[k,n] = n-th term of recurrence A[k,0] = 2, A[k,n] = A[k,n-1]^2 + k.

%t A[k_,0] = 2; A[k_,n_] := A[k,n] = A[k, n-1]^2 + k; a[n_] := A[n, n]; a /@ Range[0, 6] (* _Giovanni Resta_, Jun 20 2016 *)

%Y Cf. A001146, A003095, A003096, A062013.

%K easy,nonn

%O 0,1

%A _Jonathan Vos Post_, Dec 09 2007

%E Corrected and edited by _Giovanni Resta_, Jun 20 2016