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A167479
Convolution of the Catalan numbers A000108(n) and (-2)^n.
1
1, -1, 4, -3, 20, 2, 128, 173, 1084, 2694, 11408, 35970, 136072, 470756, 1732928, 6228989, 22899692, 83845406, 309947888, 1147367414, 4269385592, 15927495836, 59627571968, 223804469714, 842295207896, 3177355985660, 12012641100832
OFFSET
0,3
COMMENTS
Hankel transform is A079935.
FORMULA
G.f.: c(x)/(1+2x), c(x) the g.f. of A000108.
a(n) = Sum_{k=0..n} (-2)^(n-k)*A000108(k).
(n+1)*a(n) + 2*(2-n)*a(n-1) + 4*(1-2*n)*a(n-2)=0. - R. J. Mathar, Nov 16 2011 [Proof in Ekhad/Yang, Theorem 26]
a(n) ~ 2^(2*n + 1) / (3 * sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Mar 08 2018
MATHEMATICA
CoefficientList[Series[(1 - Sqrt[1 - 4*t])/(2*t*(1 + 2*t)), {t, 0, 50}], t] (* G. C. Greubel, Jun 13 2016 *)
CROSSREFS
Sequence in context: A178417 A178628 A345125 * A278424 A278662 A220861
KEYWORD
easy,sign
AUTHOR
Paul Barry, Nov 04 2009
STATUS
approved