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
Links
- G. C. Greubel, Table of n, a(n) for n = 0..725
Programs
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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
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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
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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 *) -
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
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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
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
Extensions
Edited by N. J. A. Sloane, Sep 17 2006
Corrected and offset changed by G. C. Greubel, Oct 04 2019