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%I #5 Nov 17 2018 07:33:11
%S 1,3,22,195,1946,20790,232716,2693691,31979090,387243714,4764470932,
%T 59391201870,748472730628,9520446996300,122067269204760,
%U 1575965219205195,20470515781159170,267325017886787850
%N Products of A007482 and Catalan numbers: a(n) = A007482(n)*A000108(n).
%C Radius of convergence: r = (sqrt(17)-3)/16; A(r) = sqrt(2+6/sqrt(17)). Recurrence of A007482 is A007482(n) = 3*A007482(n-1) + 2*A007482(n-2). More generally, given {S} such that: S(n) = b*S(n-1) + c*S(n-2), |b|>0, |c|>0, then Sum_{n>=0} S(n)*Catalan(n)*x^n = sqrt( (1-2*b*x - sqrt(1-4*b*x-16*c*x^2))/(2*b^2+8*c) )/x.
%F G.f.: A(x) = sqrt((1-6*x - sqrt(1-12*x-32*x^2))/34 )/x.
%F n*(n+1)*a(n) -6*n*(2*n-1)*a(n-1) -8*(2*n-1)*(2*n-3)*a(n-2)=0. - _R. J. Mathar_, Nov 17 2018
%e Begins: {1*1, 3*1, 11*2, 39*5, 139*14, 495*42, 1763*132, 6279*429,...}.
%o (PARI) {a(n)=binomial(2*n,n)/(n+1)*((3+sqrt(17))^(n+1)-(3-sqrt(17))^(n+1))/2^(n+1)/sqrt(17)}
%Y Cf. A007482, A000108, A098614, A098616, A098619.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Oct 09 2004
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