cp's OEIS Frontend

A106539 a(1)=1, a(2)=1, a(n) = (n-1)*a(n-1) - (n-2)*a(n-2) - ... - a(1) for n>=3.

%I A106539 #16 Sep 08 2022 08:45:18
%S A106539 1,1,1,0,-6,-36,-192,-1104,-7248,-54816,-472512,-4573824,-49064448,
%T A106539 -577130496,-7381281792,-101940854784,-1511556077568,-23945902043136,
%U A106539 -403579232182272,-7209532170092544,-136064164749017088,-2705030337674674176,-56501002847058788352
%N A106539 a(1)=1, a(2)=1, a(n) = (n-1)*a(n-1) - (n-2)*a(n-2) - ... - a(1) for n>=3.
%C A106539 Beginning with a(0)=0, a(1)=1 gives 0, 1, 2, 4, 8, 16, ..., 2^(n-1).
%H A106539 G. C. Greubel, <a href="/A106539/b106539.txt">Table of n, a(n) for n = 1..400</a>
%F A106539 D-finite with recurrence: a(n) = n*a(n-1) - 2*(n-2)*a(n-2), a(1)=1, a(2)=1. - _Georg Fischer_, Jun 18 2021
%F A106539 a(n) = e^(-2)*( - Gamma(n)*E_{n}(-2) + 2^(n-1)*(-Ei(2) + e^2 - Pi*i), where Ei(x) and E_{n}(x) are exponential integrals. - _G. C. Greubel_, Sep 03 2021
%e A106539 a(7) = 6*(-36) - 5(-6) - 4*0 - 3*1 - 2*1 - 1*1 = -216 + 30 - 0 - 3 - 2 - 1 = -192.
%p A106539 nmax:=24; a[1]:=1: a[2]:=1: for n from 3 to nmax do a[n]:=(n-1)*a[n-1]-add(k*a[k],k=1..n-2) od: seq(a[n],n=1..nmax); # _Emeric Deutsch_, Feb 03 2006
%t A106539 RecurrenceTable[{a[n]==n*a[n-1] - 2*(n-2)*a[n-2], a[1]==a[2]==1}, a[n], {n,1,20}] (* _Georg Fischer_, Jun 18 2021 *)
%o A106539 (Magma) [n le 2 select 1 else n*Self(n-1) - 2*(n-2)*Self(n-2): n in [1..30]]; // _G. C. Greubel_, Sep 03 2021
%o A106539 (Sage)
%o A106539 def a(n): return 1 if (n<3) else n*a(n-1) - 2*(n-2)*a(n-2)
%o A106539 [a(n) for n in (1..30)] # _G. C. Greubel_, Sep 03 2021
%Y A106539 Cf. A001571.
%K A106539 easy,sign
%O A106539 1,5
%A A106539 _Alexandre Wajnberg_, May 08 2005
%E A106539 More terms from _Emeric Deutsch_, Feb 03 2006
%E A106539 Definition adapted to offset by _Georg Fischer_, Jun 18 2021