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%I #14 Mar 15 2014 05:11:52
%S 1,3,13,67,377,2235,13701,85947,548209,3540851,23093885,151793203,
%T 1004023273,6675725867,44581355765,298829626795,2009477057761,
%U 13550281076451,91594501130989,620471833255971,4211165312423001
%N Expansion of -(3*x^5+sqrt(-7*x^2-6*x+1)*(3*x^4+5*x^3-11*x^2-7*x+2)-24*x^4-34*x^3+10*x^2+15*x-2) / (7*x^5+sqrt(-7*x^2-6*x+1)*(3*x^4+6*x^3-2*x^2+6*x-5)-15*x^4-12*x^3-12*x^2-19*x+3).
%F G.f. A(x) = G'(x)*(x*G(x)-x^2)/G(x)^2, where G(x) = -(x*sqrt(-7*x^2-6*x+1)+x^2-3*x)/(2*x^2+2).
%F a(n) = sum(m=1..n, (sum(k=m..n, (binomial(k,n-k)*binomial(-m+2*k-1,k-m))/k))*m*binomial(n-1,n-m)).
%F a(n) = [x^n] (F(x)^n-F(x)^(n-1)), where F(x) = A025227(x) = (3-sqrt(1-4*x-4*x^2))/2.
%o (Maxima)
%o a(n):=sum((sum((binomial(k,n-k)*binomial(-m+2*k-1,k-m))/k,k,m,n))*m*binomial(n-1,n-m),m,1,n);
%K nonn
%O 1,2
%A _Vladimir Kruchinin_, Mar 12 2014
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