A133471 a(n) = (n^2)*a(n-1) + a(n-2).

0, 1, 4, 37, 596, 14937, 538328, 26393009, 1689690904, 136891356233, 13690825314204, 1656726754374917, 238582343455302252, 40322072770700455505, 7903364845400744581232, 1778297412287938231232705, 455252040910557587940153712, 131569618120563430852935655473

Offset: 0

Author

Jonathan Vos Post, Nov 28 2007

Keywords

• easy
• nonn

Comments

Alternates between even and odd.

After a(3) = 37, which is the next prime?

Next primes are a(9) = 136891356233, a(51) = 2.5... * 10^132, a(249) = 1.7... * 10^980. - Charles R Greathouse IV, Mar 13 2015

Same as A036245 except for n=0. - Georg Fischer, Oct 07 2018

Links

• Georg Fischer, Table of n, a(n) for n = 0..255

Crossrefs

Cf. A000045, A000290, A001040.

Programs

GAP

a:=[0,1];; for n in [3..20] do a[n]:=(n-1)^2*a[n-1]+a[n-2]; od; a; # Muniru A Asiru, Oct 07 2018

Maple

A133471 := proc(n)
    if n <= 1 then
        n;
    else
        n^2*procname(n-1)+procname(n-2) ;
    end if;
end proc: # R. J. Mathar, Sep 23 2016

Mathematica

RecurrenceTable[{a[0]==0,a[1]==1,a[n]==n^2 a[n-1]+a[n-2]},a,{n,30}] (* or *) Module[{nn=20,frac},frac=Range[nn]^2;Join[{0},Table[Denominator[ FromContinuedFraction[Take[frac,n]]],{n,nn}]]] (* Harvey P. Dale, Mar 14 2015 *)

PARI

v=vector(100); v[1]=1;v[2]=4; for(n=3,#v, v[n]=n^2*v[n-1]+v[n-2]); v=concat(0,v) \\ Charles R Greathouse IV, Mar 13 2015

Extensions

Terms and definition corrected by Harvey P. Dale, Mar 13 2015