%I #35 Jan 06 2024 09:22:35

%S 1,2,6,39,1525,2325630,5408554896906,29252466072845872288372843,

%T 855706771342998810018458679815602502067088579902657

%N a(1) = 1; thereafter a(n+1) = a(n)^2 + n.

%H Indranil Ghosh, <a href="/A028300/b028300.txt">Table of n, a(n) for n = 1..13</a>

%H <a href="/index/Aa#AHSL">Index entries for sequences of form a(n+1)=a(n)^2 + ...</a>

%F a(n) ~ c^(2^n), where c = 1.2574108318043003098123273077302829405940294\ 604970047023808427877694426442... . - _Vaclav Kotesovec_, Dec 18 2014

%e a(3) = a(2)^2+2 = 4+2 = 6.

%t RecurrenceTable[{a[1]==1, a[n+1]==a[n]^2 + n}, a, {n,10}] (* _Vaclav Kotesovec_, Dec 18 2014 *)

%o (Magma) [n le 1 select 1 else Self(n-1)^2 +n-1: n in [1..14]]; // _G. C. Greubel_, Jan 03 2024

%o (SageMath)

%o def a(n): return 1 if n==1 else a(n-1)^2 + n-1 # a = A028300

%o [a(n) for n in range(1,15)] # _G. C. Greubel_, Jan 03 2024

%Y Cf. A086851, A098152, A153058, A153059, A153060.

%K nonn,easy

%O 1,2

%A A.R. Fink (fink(AT)cadvision.com)