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A143760 a(n+1) = a(n)^2 + n^2, a(1) = 1. 6
1, 2, 8, 73, 5345, 28569050, 816190617902536, 666167124752123519223995231345, 443778638100511299954105018279514127887014869775300070509089 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Let f(n+1,k) = f(n,k)^2 + k*n*f(n,k) + n^2, f(1, k) = 1:

f(n,0)=a(n), f(n,-1)=A143761(n), f(n,+1)=A143762(n),

f(n,-2)=A143763(n), f(n,+2)=A143764(n), f(n,-3)=A143765(n),

f(n,+3)=A143766(n).

LINKS

Table of n, a(n) for n=1..9.

Index entries for sequences of form a(n+1)=a(n)^2 + ... [From Reinhard Zumkeller, Sep 11 2008]

FORMULA

a(n) ~ c^(2^n), where c = 1.3076706365483739101135324977730044318963776104568586126528165276768888613... . - Vaclav Kotesovec, Dec 18 2014

MATHEMATICA

RecurrenceTable[{a[1]==1, a[n]==a[n-1]^2+(n-1)^2}, a[n], {n, 10}] (* Harvey P. Dale, May 03 2011 *)

CROSSREFS

Sequence in context: A305000 A013002 A012998 * A064605 A295373 A132039

Adjacent sequences:  A143757 A143758 A143759 * A143761 A143762 A143763

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Sep 01 2008

STATUS

approved

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Last modified January 16 04:59 EST 2022. Contains 350374 sequences. (Running on oeis4.)