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A286032 a(n) = a(n-1) - n*a(n-2); a(0) = a(1) = 1.

%I A286032 #21 Jun 20 2021 14:26:01
%S A286032 1,1,-1,-4,0,20,20,-120,-280,800,3600,-5200,-48400,19200,696800,
%T A286032 408800,-10740000,-17689600,175630400,511732800,-3000875200,
%U A286032 -13747264000,52271990400,368459062400,-886068707200,-10097545267200,12940241120000,285573963334400
%N A286032 a(n) = a(n-1) - n*a(n-2); a(0) = a(1) = 1.
%H A286032 Indranil Ghosh, <a href="/A286032/b286032.txt">Table of n, a(n) for n = 0..500</a>
%F A286032 a(n) = n! [x^n] (1 - sqrt(Pi / 2) * exp(-((x - 1)^2) / 2) * (x - 1) * (erfi((x - 1) / sqrt(2)) + erfi(1 / sqrt(2)))).
%F A286032 Generating function satisfies x^3*A'(x) + (2*x^2-x+1)*A(x) = 1.
%p A286032 a := proc(n) option remember;
%p A286032 if n <= 1 then 1 else a(n-1) - n*a(n-2) fi end:
%p A286032 seq(a(n), n = 0..27);
%p A286032 a_list := proc(len) 1 - sqrt(Pi/2)*exp(-((x-1)^2)/2)*(x-1)*
%p A286032 (erfi((x-1)/sqrt(2)) + erfi(1/sqrt(2))); series(%, x, len+2):
%p A286032 seq(n!*simplify(coeff(%,x,n)),n=0..len-1) end: a_list(27);
%t A286032 l={1, 1}; Do[AppendTo[l, l[[-1]] - n*l[[-2]]], {n, 2, 30}]; l (* _Indranil Ghosh_, May 01 2017 *)
%t A286032 RecurrenceTable[{a[0]==a[1]==1,a[n]==a[n-1]-n a[n-2]},a,{n,40}] (* _Harvey P. Dale_, Jun 20 2021 *)
%o A286032 (Python)
%o A286032 l=[1, 1]
%o A286032 a=b=1
%o A286032 i=2
%o A286032 while i<=30:
%o A286032     l.append(b - i*a)
%o A286032     b=l[-1]
%o A286032     a=l[-2]
%o A286032     i+=1
%o A286032 print(l) # _Indranil Ghosh_, May 01 2017
%Y A286032 Row sums of A137286.
%K A286032 sign
%O A286032 0,4
%A A286032 _Peter Luschny_, May 01 2017