A156626 a(0)=1; a(1)=2; a(2)=6; a(n+1) = 2*(n+1)*a(n) - n^2*a(n-1), n > 1.

1, 2, 6, 28, 170, 1252, 10774, 105764, 1164298, 14188468, 189461222, 2749300084, 43058394154, 723619035908, 12984464393398, 247704600763972, 5005042735932554, 106759075226130004, 2396869357456172038, 56491095210068416148, 1394373970361058540202

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..442

Maple

A156626 := proc(n)
        if n<=1 then
                n+1 ;
        elif n = 2 then
                6 ;
        else
                2*n*procname(n-1)-(n-1)^2*procname(n-2) ;
        end if;
end proc:
seq(A156626(n), n=0..20) ; # R. J. Mathar, Sep 27 2011

Mathematica

Join[{1}, RecurrenceTable[{a[n] == 2*n*a[n-1] - (n-1)^2*a[n-2], a[1] == 2, a[2] == 6}, a, {n, 1, 50}]] (* G. C. Greubel, Sep 01 2018 *)

Prog

(PARI) m=30; v=concat([2, 6], vector(m-2)); for(n=3, m, v[n] = 2*n*v[n-1]-(n-1)^2*v[n-2]); concat([1], v) \\ G. C. Greubel, Sep 01 2018
(Magma) I:=[2, 6]; [1] cat [n le 2 select I[n] else 2*n*Self(n-1) - (n-1)^2*Self(n-2): n in [1..30]]; // G. C. Greubel, Sep 01 2018

Crossrefs

Cf. A001620, A002720.

Sequence in context: A262002 A245633 A345367 * A207386 A088501 A140092

Adjacent sequences: A156623 A156624 A156625 * A156627 A156628 A156629

Keyword

easy,nonn

Author

Jonathan Vos Post, Feb 12 2009

Status

approved