STATUS
reviewed
approved
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Revision History for A009102
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proposed
reviewed
STATUS
editing
proposed
FORMULA
Recurrence: a(0) = 1, a(1) = -1, a(2) = 1, a(n+3) = -(n+3)*a(n+2)-a(n+1)-(n+1)*a(n). (End)
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proposed
editing
STATUS
editing
proposed
FORMULA
a(n) = (-1)^n * n! * Sum_{k=0..floor(n/2)} (-1)^k/(2k)!. Unsigned sequence satisfies e.g.f. cos(x)/(1-x). - Ralf Stephan, Apr 16 2004
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approved
editing
STATUS
editing
approved
MATHEMATICA
With[{nn=20}, CoefficientList[Series[Cos[x]/(1+x), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Feb 18 2024 *)
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approved
editing
PROG
(MAGMAMagma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Cos(x)/(1+x))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Jul 26 2018
STATUS
proposed
approved