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URL: https://oeis.org/A168298

⇱ A168298 - OEIS

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A168298
a(n) = 1 - n^2*2^n.
2
1, -1, -15, -71, -255, -799, -2303, -6271, -16383, -41471, -102399, -247807, -589823, -1384447, -3211263, -7372799, -16777215, -37879807, -84934655, -189267967, -419430399, -924844031, -2030043135, -4437573631, -9663676415, -20971519999, -45365592063
OFFSET
0,3
COMMENTS
Numerator of 2^(-n) - n^2.
FORMULA
a(n)= 7*a(n-1) -18*a(n-2) +20*a(n-3) -8*a(n-4) = 1-A007758(n). - R. J. Mathar, Nov 24 2009
G.f.: -(4*x^3-10*x^2+8*x-1) / ((x-1)*(2*x-1)^3). - Colin Barker, Feb 10 2015
E.g.f.: exp(x) - 2*x*(1 + 2*x)*exp(2*x). - G. C. Greubel, Jul 17 2016
MATHEMATICA
f[n_]:=2^n-n^2; Table[Numerator[f[n]], {n, 0, -50, -1}]
LinearRecurrence[{7, -18, 20, -8}, {1, -1, -15, -71}, 30] (* Harvey P. Dale, May 14 2019 *)
PROG
(PARI) Vec(-(4*x^3-10*x^2+8*x-1)/((x-1)*(2*x-1)^3) + O(x^100)) \\ Colin Barker, Feb 10 2015
(Magma) [1-n^2*2^n: n in [0..30]]; // Vincenzo Librandi, Jul 18 2016
CROSSREFS
Sequence in context: A253476 A308596 A145053 * A126274 A241234 A212097
KEYWORD
sign,easy
AUTHOR
EXTENSIONS
Offset corrected, keyword:sign added, and definition simplified by R. J. Mathar, Nov 23 2009
STATUS
approved