A122033 a(n) = 2*a(n-1) - 2*(n-2)*a(n-2), with a(0)=1, a(1)=2.

1, 2, 4, 4, -8, -40, -16, 368, 928, -3296, -21440, 16448, 461696, 561536, -9957632, -34515200, 209783296, 1455022592, -3803020288, -57076808704, 22755112960, 2214428956672, 3518653394944, -85968709390336, -326758168158208, 3301044295639040, 22286480662872064

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..725

Formula

a(n) = 2*a(n-1) - 2*(n-2)*a(n-2), with a(0)=1, a(1)=2. - G. C. Greubel, Oct 04 2019

a(n) = 2*A062267(n-1) for n > 0. - Michel Marcus, Oct 05 2019

E.g.f.: 1 + exp(1)*sqrt(Pi)*( erf(1) - erf(1-x) ), where erf(x) is the error function. - G. C. Greubel, Oct 05 2019

Maple

a:= proc(n) option remember;
      if n < 2 then n+1
    else 2*(a(n-1) - (n-2)*a(n-2))
      fi
    end proc:
seq(a(n), n = 0..35); # G. C. Greubel, Oct 04 2019

Mathematica

a[n_]:= a[n]= If[n<2, n+1, a[n-1]-(n-2)*a[n-2]]; Table[a[n], {n, 0, 30}] (* modified by G. C. Greubel, Oct 04 2019 *)
nxt[{n_, a_, b_}]:={n+1, b, 2b-2a(n-1)}; NestList[nxt, {1, 1, 2}, 30][[;; , 2]] (* Harvey P. Dale, Jan 01 2024 *)

Prog

(PARI) my(m=35, v=concat([1, 2], vector(m-2))); for(n=3, m, v[n] = 2*(v[n-1] - (n-3)*v[n-2] ) ); v \\ G. C. Greubel, Oct 04 2019
(Magma) I:=[1, 2]; [n le 2 select I[n] else 2*(Self(n-1)-(n-3)*Self(n-2)): n in [1..35]]; // G. C. Greubel, Oct 04 2019
(Sage)
def a(n):
    if n<2: return n+1
    else: return 2*(a(n-1) - (n-2)*a(n-2))
[a(n) for n in (0..35)] # G. C. Greubel, Oct 04 2019
(GAP) a:=[1, 2];; for n in [3..35] do a[n]:=2*(a[n-1]-(n-3)*a[n-2]); od; a; # G. C. Greubel, Oct 04 2019

Crossrefs

Cf. A000898, A121966, A328141.

Sequence in context: A296229 A322175 A298117 * A281122 A201777 A096189

Adjacent sequences: A122030 A122031 A122032 * A122034 A122035 A122036

Keyword

sign,less

Author

Roger L. Bagula, Sep 13 2006

Extensions

Edited by N. J. A. Sloane, Sep 17 2006

Corrected and offset changed by G. C. Greubel, Oct 04 2019

Status

approved