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%I #21 Aug 15 2017 03:22:51
%S 1,2,3,10,57,446,4403,52390,729057,11612522,208296339,4154314258,
%T 91186617337,2184324501830,56701250430243,1585450687544974,
%U 47506819375918977,1518632769341862290,51586007338247398883
%N a(0)=1; a(1)=2; a(n+1) = 2*n*a(n) - a(n-1) for n >= 1.
%C a(n) = (a(n-1) + a(n+1))/(2n). - _Emeric Deutsch_, Feb 03 2006
%H Vincenzo Librandi, <a href="/A093856/b093856.txt">Table of n, a(n) for n = 0..200</a>
%F a(-n) = (-1)^n * a(n). - _Michael Somos_, Jan 25 2014
%F a(n+1) ~ 1.0903447... * 2^n * n! * f(1/(4*n)) where f(x) = 1 + x + x^2/2! + 13*x^3/3! + 241*x^4/4! + 6201*x^5/5! + ...). - _Michael Somos_, Jan 26 2014
%F 0 = a(n) * (a(n+2)) + a(n+1) * (-a(n+1) + 2*a(n+2) - a(n+3)) + a(n+2) * (a(n+2)) for all n in Z. - _Michael Somos_, Jan 25 2014
%F 0 = u0 * u3 - u1 * (u2 + 2*u3) + u2 * (4*u2) where u0 = e.g.f. a(n), u1=u0', u2=u1', u3=u2'. - _Michael Somos_, Jan 25 2014
%e a(3) = 2*2*a(2)-a(1) = 12-2 = 10.
%e G.f. = 1 + 2*x + 3*x^2 + 10*x^3 + 57*x^4 + 446*x^5 + 4403*x^6 + 52390*x^7 + ...
%p a[0]:=1: a[1]:=2: for n from 1 to 20 do a[n+1]:=2*n*a[n]-a[n-1] od: seq(a[n],n=0..20); # _Emeric Deutsch_, Feb 03 2006
%t RecurrenceTable[{a[0]==1,a[1]==2,a[n]==2(n-1)*a[n-1]-a[n-2]},a,{n,20}] (* _Harvey P. Dale_, May 31 2016 *)
%K easy,nonn
%O 0,2
%A _Amarnath Murthy_, Apr 19 2004
%E More terms from _Emeric Deutsch_, Feb 03 2006
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