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A116390
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Expansion of 1/(2*sqrt(1-4*x^2)-x-1).
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1
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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
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OFFSET
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0,3
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REFERENCES
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Hankel transform is 4^n. [From Paul Barry, Jan 19 2011]
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LINKS
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Table of n, a(n) for n=0..26.
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FORMULA
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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
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EXAMPLE
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Row sums of number triangle A116389.
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CROSSREFS
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Sequence in context: A049602 A119031 A034435 * A028351 A211952 A098640
Adjacent sequences: A116387 A116388 A116389 * A116391 A116392 A116393
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry, Feb 12 2006
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STATUS
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approved
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