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A127275
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Expansion of (sqrt(1-4x)-x)/(1-4x).
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5
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1, 1, 2, 4, 6, -4, -100, -664, -3514, -16916, -77388, -343144, -1490148, -6376616, -26992264, -113317936, -472661434, -1961361076, -8104733884, -33374212936, -137031378124, -561253753336, -2293947547384, -9358755316816, -38121140494564, -155064370272904
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OFFSET
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0,3
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COMMENTS
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Hankel transform is A127276.
The second self-composition of the g.f. G(x) of A120009 is G(G(x)) = (sqrt(1-4x)-x)/(1-4x) - 1.
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LINKS
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Table of n, a(n) for n=0..25.
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FORMULA
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a(n)=C(2n,n)-4^(n-1)+0^n/4. - Paul Barry, Jan 10 2007
Conjecture: n*a(n) +2*(-4*n+3)*a(n-1) +8*(2*n-3)*a(n-2)=0. - R. J. Mathar, Nov 26 2012
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EXAMPLE
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A(x) = 1 + x + 2*x^2 + 4*x^3 + 6*x^4 - 4*x^5 - 100*x^6 - 664*x^7 +...
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PROG
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(PARI) {a(n)=local(k=2, x=X+X^3*O(X^n)); polcoeff( x*((1-k+k^2)-k^2*(k+1)*x-k*(1-(k+2)*x)*(1-sqrt(1-4*x))/2/x)/(1-k+k^2*x)^2, n, X)}
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CROSSREFS
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Cf. A120009, A120012 (3-rd self-composition); A000108 (Catalan).
Sequence in context: A151886 A099784 A082747 * A071288 A063892 A022485
Adjacent sequences: A127272 A127273 A127274 * A127276 A127277 A127278
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KEYWORD
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easy,sign
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AUTHOR
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Paul D. Hanna, Jun 07 2006
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EXTENSIONS
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Definition revised by Paul Barry, Jan 10 2007
Edited by N. J. A. Sloane, Jul 03 2008 at the suggestion of R. J. Mathar and Max Alekseyev
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STATUS
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approved
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