%I #6 Aug 25 2013 14:16:54
%S 1,3,10,33,110,372,1276,4433,15574,55250,197676,712538,2585292,
%T 9434830,34610400,127553745,472055910,1753616370,6536826780,
%U 24443315550,91664179620,344655239760,1299052403688,4907335827258,18576824685820
%N Expansion of (1+x^2*C^2)*C^3, where C = (1-(1-4*x)^(1/2))/(2*x) is g.f. for Catalan numbers, A000108.
%F Conjecture: 2*(n+3)*a(n) +4*(-3*n-4)*a(n-1) +(17*n-9)*a(n-2) +2*(-2*n+5)*a(n-3)=0. - _R. J. Mathar_, Aug 25 2013
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Jun 06 2002
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