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 A240880 Expansion of g.f.: (-1 + sqrt(1+12*x+48*x^2)) / (6*x). 3
 1, 1, -6, 33, -162, 666, -1836, -2079, 79542, -741474, 4907628, -24837030, 82449900, 53319060, -3741922008, 38613958497, -274566158298, 1475669401398, -5211777090564, -2356585871778, 240686500011588, -2593621485808596, 19047621883804056, -105353643788834598 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS This sequence is the member (q=-3) of a class of generalized Catalan numbers (see A000108), with g.f. (1-sqrt(1-q*4*x*(1-(q-1)*x)))/(2*q*x), q<>0. LINKS Fung Lam, Table of n, a(n) for n = 0..1000 FORMULA G.f.: (-1 + sqrt(1+12*x+48*x^2)) / (6*x). D-finite with recurrence: (n+3)*a(n+2)+6*(2*n+3)*a(n+1)+48*n*a(n)=0, a(0)=1, a(1)=1. Lim sup n->infinity |a(n)|^(1/n) = 4*sqrt(3) = 6.9282... - Vaclav Kotesovec, May 02 2014 a(n) ~ 3^(n/2-1)*4^n / (n^(3/2)*sqrt(Pi)) * (sqrt(3)*cos(5*Pi*n/6) + 3*sin(5*Pi*n/6) - (15*sqrt(3)*cos(5*Pi*n/6) + 9*sin(5*Pi*n/6))/(8*n)). - Vaclav Kotesovec, May 02 2014 CROSSREFS Cf. A000108, A258723. Sequence in context: A266944 A301272 A290921 * A099432 A072260 A281930 Adjacent sequences:  A240877 A240878 A240879 * A240881 A240882 A240883 KEYWORD sign,easy AUTHOR Fung Lam, May 01 2014 STATUS approved

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Last modified April 7 04:20 EDT 2020. Contains 333292 sequences. (Running on oeis4.)