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 A116390 Expansion of 1/(2*sqrt(1-4*x^2)-x-1). 1
 1, 1, 5, 9, 33, 73, 233, 569, 1693, 4353, 12477, 32985, 92637, 248673, 690549, 1869513, 5158881, 14033161, 38587193, 105246041, 288818305, 788939769, 2162574513, 5912375033, 16196093881, 44300854441, 121311490937 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 REFERENCES Hankel transform is 4^n. [From Paul Barry, Jan 19 2011] LINKS FORMULA a(n)=sum(k=0..n, sum(j=0..k, C(k,j)*(-1)^(k-j) * sum(i=0..floor(n/2), C(i+(j-1)/2,i)*C(j,n-2*i)*4^i ) ) ). a(n)=sum(k=0..floor((n+1)/2), (C(n,k)-C(n,k-1))*A006130(n-2*k) ). [From Paul Barry, Jan 19 2011] Starting with offset 1, let M = an infinite tridiagonal matrix with [1,0,0,0,...] in the main diagonal and [2,1,1,1,...] in the super and subdiagonals. Let V = vector [1,0,0,0,...]. The sequence = iterates of M*V as to the leftmost column. [From Gary W. Adamson, Jun 08 2011]. conjecture: -3*n*a(n)+2*n*a(n-1)+(29*n-36)*a(n-2) +8*(3-n)*a(n-3) +68*(3-n)*a(n-4)=0. - R. J. Mathar, Aug 09 2012 EXAMPLE Row sums of number triangle A116389. CROSSREFS Sequence in context: A049602 A119031 A034435 * A028351 A211952 A098640 Adjacent sequences:  A116387 A116388 A116389 * A116391 A116392 A116393 KEYWORD easy,nonn AUTHOR Paul Barry, Feb 12 2006 STATUS approved

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