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

0,2

Comments

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

Links

G. C. Greubel, Table of n, a(n) for n = 0..800

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.

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);

Mathematica

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

Prog

(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
(Magma) I:=[1, 2]; [n le 2 select I[n] else Self(n-1) - (n-3)*Self(n-2): n in [1..35]];
(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)]
(GAP) a:=[1, 2];; for n in [3..35] do a[n]:=a[n-1]-(n-3)*a[n-2]; od; a;

Crossrefs

Cf. A001464, A060821, A121966, A122033.

Sequence in context: A308720 A086882 A341415 * A168587 A320119 A100240

Adjacent sequences: A328138 A328139 A328140 * A328142 A328143 A328144

Keyword

sign

Author

G. C. Greubel, Oct 04 2019

Status

approved