A328141 a(n) = a(n-1) - (n-2)*a(n-2), with a(0)=1, a(1)=2.
1, 2, 2, 0, -4, -4, 12, 32, -40, -264, 56, 2432, 1872, -24880, -47344, 276096, 938912, -3202528, -18225120, 36217856, 364270016, -323869248, -7609269568, -808015360, 166595915136, 185180268416, -3813121694848, -8442628405248, 90698535660800, 318649502602496, -2220909495899904
Offset: 0
Keywords
Links
- G. C. Greubel, Table of n, a(n) for n = 0..800
Programs
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GAP
a:=[1,2];; for n in [3..35] do a[n]:=a[n-1]-(n-3)*a[n-2]; od; a;
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Magma
I:=[1,2]; [n le 2 select I[n] else Self(n-1) - (n-3)*Self(n-2): n in [1..35]];
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Maple
a:= proc (n) option remember; if n < 2 then n+1 else a(n-1) - (n-2)*a(n-2) fi; end proc; seq(a(n), n = 0..35);
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Mathematica
a[n_]:= a[n]= If[n<2, n+1, a[n-1]-(n-2)*a[n-2]]; Table[a[n], {n,0,35}] -
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
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Sage
def a(n): if n<2: return n+1 else: return a(n-1) - (n-2)*a(n-2) [a(n) for n in (0..35)]
Formula
a(n) = a(n-1) - (n-2)*a(n-2), with a(0)=1, a(1)=2.
E.g.f.: 1 + sqrt(2*e*Pi)*( erf(1/sqrt(2)) + erf((x-1)/sqrt(2)) ), where erf(x) is the error function.
a(n) = 2*(-1)^(n-1)*A001464(n-1).
a(n) = 2*(1/sqrt(2))^(n-1) * Hermite(n-1, 1/sqrt(2)), n > 0.
Comments