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%I #11 Jun 11 2018 05:53:43
%S 1,4,15,54,192,682,2431,8710,31382,113696,414086,1515516,5571750,
%T 20569590,76228095,283481670,1057628550,3957577800,14849601090,
%U 55859886420,210622646520,795898303668,3013646759910,11432740177564,43448822603452,165396657221152
%N Expansion of (1+x^2*C^2)*C^4, where C = (1-(1-4*x)^(1/2))/(2*x) is g.f. for Catalan numbers, A000108.
%F a(n) = (Sum_{k=0..n} (k+1)*(k^2+k+1)*binomial(2*n-k,n))/(n+1). - _Vladimir Kruchinin_, Sep 28 2011
%o (Maxima) a(n):=sum((k+1)*(k^2+k+1)*binomial(2*n-k,n),k,0,n)/(n+1); /* _Vladimir Kruchinin_, Sep 28 2011 */
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Jun 06 2002
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