A143765 a(n+1) = a(n)^2 - 3*n*a(n) + n^2, a(1) = 1.

1, -1, 11, 31, 605, 356975, 127424725111, 16237060566937994735039, 263642135854412795003324875413502371940690649, 69507175797876652622009028770643203522181284529919017784559264153993383198392412717393759

Offset

1,3

Comments

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

f(n,0)=A143760(n), f(n,-1)=A143761(n), f(n,+1)=A143762(n),

f(n,-2)=A143763(n), f(n,+2)=A143764(n), f(n,-3)=a(n), f(n,+3)=A143766(n).

Links

Table of n, a(n) for n=1..10.

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 = 1.22112407764058519321076802441458002508833724488233983960016657090909521541... . - Vaclav Kotesovec, Dec 18 2014

Mathematica

RecurrenceTable[{a[n+1] == a[n]^2 - 3*n*a[n] + n^2, a[1] == 1}, a, {n, 1, 10}] (* Vaclav Kotesovec, Dec 18 2014 *)

Crossrefs

Sequence in context: A163763 A201808 A111015 * A023306 A068839 A228530

Adjacent sequences: A143762 A143763 A143764 * A143766 A143767 A143768

Keyword

sign

Author

Reinhard Zumkeller, Sep 01 2008

Status

approved