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A082472 a(1) = 1, a(n) = Sum_{k=1..n-1} a(k)*2^k.

%I A082472 #36 Jun 05 2020 06:03:34
%S A082472 1,2,10,90,1530,50490,3281850,423358650,108803173050,55816027774650,
%T A082472 57211428469016250,117226216933014296250,480275810774559571736250,
%U A082472 3934899717675966571235096250,64473331874120712269687052056250
%N A082472 a(1) = 1, a(n) = Sum_{k=1..n-1} a(k)*2^k.
%H A082472 Vincenzo Librandi, <a href="/A082472/b082472.txt">Table of n, a(n) for n = 1..80</a>
%F A082472 a(n+1) = (2^n+1)*a(n) for n>=2.
%F A082472 a(n) is asymptotic to c*2^(n*(n-1)/2) where c = Product_{k>=1} (1+1/(2*2^k)) = 1.5894873526.....
%F A082472 c = 2*A079555/3. - _Vaclav Kotesovec_, Jun 05 2020
%F A082472 G.f. A(x) satisfies: A(x) = x * (1 + A(2*x) / (1 - x)). - _Ilya Gutkovskiy_, Jun 04 2020
%t A082472 Join[{1},RecurrenceTable[{a[1]==2,a[n]==(1+2^n) a[-1+n]},a[n], {n,15}]] (* _Harvey P. Dale_, May 11 2011 *)
%o A082472 (Sage)
%o A082472 from ore_algebra import *
%o A082472 R.<x> = QQ['x']; A.<Qx> = OreAlgebra(R, 'Qx', q=2)
%o A082472 print((Qx - x - 1).to_list([0,1,2], 10)) # _Ralf Stephan_, Apr 24 2014
%Y A082472 Cf. A005329, A079555.
%K A082472 nonn
%O A082472 1,2
%A A082472 _Benoit Cloitre_, Apr 27 2003