A028300 a(1) = 1; thereafter a(n+1) = a(n)^2 + n.

1, 2, 6, 39, 1525, 2325630, 5408554896906, 29252466072845872288372843, 855706771342998810018458679815602502067088579902657

Offset: 1

Author

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

Keywords

• nonn
• easy

Examples

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

Links

• Indranil Ghosh, Table of n, a(n) for n = 1..13
• Index entries for sequences of form a(n+1)=a(n)^2 + ...

Crossrefs

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

Programs

Magma

[n le 1 select 1 else Self(n-1)^2 +n-1: n in [1..14]]; // G. C. Greubel, Jan 03 2024

Mathematica

RecurrenceTable[{a[1]==1, a[n+1]==a[n]^2 + n}, a, {n,10}] (* Vaclav Kotesovec, Dec 18 2014 *)

SageMath

def a(n): return 1 if n==1 else a(n-1)^2 + n-1 # a = A028300
[a(n) for n in range(1,15)] # G. C. Greubel, Jan 03 2024

Formula

a(n) ~ c^(2^n), where c = 1.2574108318043003098123273077302829405940294\ 604970047023808427877694426442... . - Vaclav Kotesovec, Dec 18 2014