A166228 Alternating sum of large Schroeder numbers.

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

Vincenzo Librandi, Table of n, a(n) for n = 0..300

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

Adjacent sequences: A166225 A166226 A166227 * A166229 A166230 A166231

Keyword

easy,nonn

Author

Paul Barry, Oct 09 2009

Status

approved