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 A127275 Expansion of (sqrt(1-4x)-x)/(1-4x). 5
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 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. LINKS FORMULA 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 EXAMPLE A(x) = 1 + x + 2*x^2 + 4*x^3 + 6*x^4 - 4*x^5 - 100*x^6 - 664*x^7 +... PROG (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)} CROSSREFS Cf. A120009, A120012 (3rd self-composition); A000108 (Catalan). Sequence in context: A257080 A099784 A082747 * A242796 A298527 A071288 Adjacent sequences:  A127272 A127273 A127274 * A127276 A127277 A127278 KEYWORD easy,sign AUTHOR Paul D. Hanna, Jun 07 2006 EXTENSIONS 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 STATUS approved

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Last modified June 6 18:59 EDT 2020. Contains 334832 sequences. (Running on oeis4.)