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A006589
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a(n) = (n+3)*2^n - 1.
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6
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0, 2, 7, 19, 47, 111, 255, 575, 1279, 2815, 6143, 13311, 28671, 61439, 131071, 278527, 589823, 1245183, 2621439, 5505023, 11534335, 24117247, 50331647, 104857599, 218103807, 452984831, 939524095
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OFFSET
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-1,2
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COMMENTS
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Binomial transform of [2/1, 3/2, 4/3, 5/4, ...] = 2/1, 7/2, 19/3, 47/4, 111/5, ... - Gary W. Adamson, Apr 28 2005
Binomial transform of A087156 := [0,2,3,4,5,6,7,8,9,10,...]. - Philippe Deléham, Nov 25 2008
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REFERENCES
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W. A. Whitworth, DCC Exercises in Choice and Chance, Stechert, NY, 1945, p. 28.
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LINKS
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FORMULA
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G.f.: (2-3*x)/((1-x)*(1-2*x)^2).
a(n) = 5*a(n-1) - 8*a(n-2) + 4*a(n-3). (End)
a(n) = Sum_{k=0..n} Sum_{i=0..n} (binomial(n,i) + binomial(k,i)). - Wesley Ivan Hurt, Sep 21 2017
E.g.f.: (3 + 2*x)*exp(2*x) - exp(x). - G. C. Greubel, Jul 07 2021
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MATHEMATICA
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Table[2^n*(n+3) -1, {n, -1, 30}] (* G. C. Greubel, Jul 07 2021 *)
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PROG
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(Sage) [2^n*(n+3) -1 for n in (-1..30)] # G. C. Greubel, Jul 07 2021
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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