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A103821
A Whitney transform of the central binomial coefficients A000984.
1
1, 3, 11, 43, 179, 771, 3395, 15171, 68515, 311907, 1428835, 6578531, 30414435, 141105251, 656588899, 3063038051, 14321092195, 67088405091, 314825048675, 1479654425187, 6963888239203, 32815960756835, 154813864252003
OFFSET
0,2
COMMENTS
Partial sums of A006139. The Whitney transform maps the sequence with g.f. g(x) to that with g.f. (1/(1-x))g(x(1+x)).
LINKS
FORMULA
G.f. : 1/((1-x)sqrt(1-4x-4x^2));
a(n)=sum{k=0..n, sum{i=0..n, C(k, i-k)}*C(2k, k)}.
Conjecture: n*a(n) +(2-5n)*a(n-1) +2*a(n-2)+4*(n-1)*a(n-3)=0. - R. J. Mathar, Dec 14 2011
a(n) ~ sqrt(34+23*sqrt(2))*(2+2*sqrt(2))^n/(7*sqrt(Pi*n)). - Vaclav Kotesovec, Oct 17 2012
MATHEMATICA
CoefficientList[Series[1/((1-x)*Sqrt[1-4*x-4*x^2]), {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 17 2012 *)
CROSSREFS
Sequence in context: A151093 A151094 A339043 * A151095 A219262 A196151
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Feb 16 2005
STATUS
approved