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A120580
Hankel transform of Sum_{k=0..n} C(2k,k).
4
1, 0, -4, -8, 0, 32, 64, 0, -256, -512, 0, 2048, 4096, 0, -16384, -32768, 0, 131072, 262144, 0, -1048576, -2097152, 0, 8388608, 16777216, 0, -67108864, -134217728, 0, 536870912, 1073741824, 0, -4294967296, -8589934592, 0, 34359738368, 68719476736, 0, -274877906944, -549755813888, 0
OFFSET
0,3
COMMENTS
Hankel transform of A006134.
Hankel transform of A098479. - Paul Barry, Sep 19 2008
Hankel transform of A025565. - Paul Barry, Mar 26 2010
FORMULA
G.f.: (1-2x)/(1-2x+4x^2).
a(n) = 2^n*(cos(Pi*n/3)-sin(Pi*n/3)/sqrt(3)).
E.g.f.: exp(x)*(cos(sqrt(3)*x) - sin(sqrt(3)*x)/sqrt(3)). - Stefano Spezia, Jul 15 2024
MATHEMATICA
LinearRecurrence[{2, -4}, {1, 0}, 50] (* Harvey P. Dale, Feb 13 2023 *)
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Paul Barry, Jun 15 2006
STATUS
approved