A143762 a(n+1) = a(n)^2 + n*a(n) + n^2, a(1) = 1.

1, 3, 19, 427, 184053, 33876427099, 1147612313197120118431, 1317014021401644919149757309088631306730827, 1734525932568532421128602190712731410907662021613907396581559184320372648524685950609

Offset: 1

Author

Reinhard Zumkeller, Sep 01 2008

Keywords

• nonn

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)=a(n),

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

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

Links

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

Programs

Mathematica

RecurrenceTable[{a[n+1] == a[n]^2 + n*a[n] + n^2, a[1] == 1}, a, {n, 1, 10}] (* Vaclav Kotesovec, Dec 18 2014 *)
nxt[{n_, a_}] := {n + 1, a^2 + n*a + n^2}; NestList[nxt,{1,1},10][[All,2]] (* Harvey P. Dale, Sep 12 2018 *)

Formula

a(n) ~ c^(2^n), where c = 1.460594463210996899745335217057197049886968082959330102210304982704405107261... . - Vaclav Kotesovec, Dec 18 2014