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A166228
Alternating sum of large Schroeder numbers.
3
1, 1, 5, 17, 73, 321, 1485, 7073, 34513, 171585, 866133, 4427313, 22870425, 119208321, 626178717, 3311424321, 17615732385, 94202293633, 506116560293, 2730607756881, 14788011564009, 80361643637953, 438070231780973
OFFSET
0,3
COMMENTS
Hankel transform is A166231. Binomial transform is A166229.
LINKS
FORMULA
G.f.: (1-x-sqrt(1-6x+x^2))/(2x(1+x));
a(n) = Sum{k=0..n} (-1)^k*A006318(n-k) = Sum_{k=0..n} (-1)^(n-k)*A006318(k).
Conjecture: (n+1)*a(n) +(4-5n)*a(n-1) +(1-5n)*a(n-2) +(n-2)*a(n-3)=0. - R. J. Mathar, Nov 17 2011
a(n) ~ sqrt(48+34*sqrt(2))*(3+2*sqrt(2))^n/(8*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 20 2012
MATHEMATICA
CoefficientList[Series[(1-x-Sqrt[1-6*x+x^2])/(2*x*(1+x)), {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 20 2012 *)
CROSSREFS
Sequence in context: A149721 A325156 A149722 * A362177 A102387 A149723
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Oct 09 2009
STATUS
approved