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%I #17 Sep 08 2022 08:46:24
%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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