|
|
A120617
|
|
Hankel transform of g.f. 1/sqrt(1+4x^2).
|
|
5
|
|
|
1, -2, -4, 8, 16, -32, -64, 128, 256, -512, -1024, 2048, 4096, -8192, -16384, 32768, 65536, -131072, -262144, 524288, 1048576, -2097152, -4194304, 8388608, 16777216, -33554432, -67108864, 134217728, 268435456, -536870912, -1073741824, 2147483648, 4294967296, -8589934592
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
Hankel transform of e.g.f. Bessel_I(0,2*sqrt(-1)*x) or (1,0,-2,0,6,0,-20,...).
Hankel transform of Sum{k=0..n} (-1)^(n-k)*C(n,k)^2.
|
|
LINKS
|
|
|
FORMULA
|
G.f.: (1-2*x)/(1+4*x^2); a(n) = 2^n*(cos(Pi*(n+1)/2)+sin(Pi*(n+1)/2)).
a(n) = ( 2*i^(n+1) )^n, where i=sqrt(-1). - Bruno Berselli, Oct 12 2011
|
|
MATHEMATICA
|
LinearRecurrence[{0, -4}, {1, -2}, 40] (* or *) CoefficientList[ Series[ (1-2x)/(1+4x^2), {x, 0, 40}], x] (* Harvey P. Dale, Oct 12 2011 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|