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A082472 a(1) = 1, a(n) = Sum_{k=1..n-1} a(k)*2^k. 1
1, 2, 10, 90, 1530, 50490, 3281850, 423358650, 108803173050, 55816027774650, 57211428469016250, 117226216933014296250, 480275810774559571736250, 3934899717675966571235096250, 64473331874120712269687052056250 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..80

FORMULA

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.....

c = 2*A079555/3. - Vaclav Kotesovec, Jun 05 2020

G.f. A(x) satisfies: A(x) = x * (1 + A(2*x) / (1 - x)). - Ilya Gutkovskiy, Jun 04 2020

MATHEMATICA

Join[{1}, RecurrenceTable[{a[1]==2, a[n]==(1+2^n) a[-1+n]}, a[n], {n, 15}]] (* Harvey P. Dale, May 11 2011 *)

PROG

(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

CROSSREFS

Cf. A005329, A079555.

Sequence in context: A320962 A067550 A086587 * A095937 A277380 A108528

Adjacent sequences:  A082469 A082470 A082471 * A082473 A082474 A082475

KEYWORD

nonn

AUTHOR

Benoit Cloitre, Apr 27 2003

STATUS

approved

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Last modified August 13 06:22 EDT 2020. Contains 336442 sequences. (Running on oeis4.)