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A328141 a(n) = a(n-1) - (n-2)*a(n-2), with a(0)=1, a(1)=2. 2


%S 1,2,2,0,-4,-4,12,32,-40,-264,56,2432,1872,-24880,-47344,276096,

%T 938912,-3202528,-18225120,36217856,364270016,-323869248,-7609269568,

%U -808015360,166595915136,185180268416,-3813121694848,-8442628405248,90698535660800,318649502602496,-2220909495899904

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

%C Former title and formula of A122033, but not the data.

%H G. C. Greubel, <a href="/A328141/b328141.txt">Table of n, a(n) for n = 0..800</a>

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

%F E.g.f.: 1 + sqrt(2*e*Pi)*( erf(1/sqrt(2)) + erf((x-1)/sqrt(2)) ), where erf(x) is the error function.

%F a(n) = 2*(-1)^(n-1)*A001464(n-1).

%F a(n) = 2*(1/sqrt(2))^(n-1) * Hermite(n-1, 1/sqrt(2)), n > 0.

%p a:= proc (n) option remember;

%p if n < 2 then n+1

%p else a(n-1) - (n-2)*a(n-2)

%p fi;

%p end proc; seq(a(n), n = 0..35);

%t a[n_]:= a[n]= If[n<2, n+1, a[n-1]-(n-2)*a[n-2]]; Table[a[n], {n,0,35}]

%o (PARI) my(m=35, v=concat([1,2], vector(m-2))); for(n=3, m, v[n] = v[n-1] - (n-3)*v[n-2] ); v

%o (MAGMA) I:=[1,2]; [n le 2 select I[n] else Self(n-1) - (n-3)*Self(n-2): n in [1..35]];

%o (Sage)

%o def a(n):

%o if n<2: return n+1

%o else: return a(n-1) - (n-2)*a(n-2)

%o [a(n) for n in (0..35)]

%o (GAP) a:=[1,2];; for n in [3..35] do a[n]:=a[n-1]-(n-3)*a[n-2]; od; a;

%Y Cf. A001464, A060821, A121966, A122033.

%K sign

%O 0,2

%A _G. C. Greubel_, Oct 04 2019

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Last modified August 14 10:58 EDT 2022. Contains 356116 sequences. (Running on oeis4.)