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A082472
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a(1) = 1, a(n) = Sum_{k=1..n-1} a(k)*2^k.
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1
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1, 2, 10, 90, 1530, 50490, 3281850, 423358650, 108803173050, 55816027774650, 57211428469016250, 117226216933014296250, 480275810774559571736250, 3934899717675966571235096250, 64473331874120712269687052056250
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n+1) = (2^n+1)*a(n) for n>=2.
a(n) is asymptotic to c*2^(n*(n-1)/2) where c = Product_{k>=1} (1+1/(2*2^k)) = 1.5894873526.....
G.f. A(x) satisfies: A(x) = x * (1 + A(2*x) / (1 - x)). - Ilya Gutkovskiy, Jun 04 2020
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MATHEMATICA
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Join[{1}, RecurrenceTable[{a[1]==2, a[n]==(1+2^n) a[-1+n]}, a[n], {n, 15}]] (* Harvey P. Dale, May 11 2011 *)
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PROG
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(Sage)
from ore_algebra import *
R.<x> = QQ['x']; A.<Qx> = OreAlgebra(R, 'Qx', q=2)
print((Qx - x - 1).to_list([0, 1, 2], 10)) # Ralf Stephan, Apr 24 2014
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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