A239198 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).
1, 3, 13, 67, 377, 2235, 13701, 85947, 548209, 3540851, 23093885, 151793203, 1004023273, 6675725867, 44581355765, 298829626795, 2009477057761, 13550281076451, 91594501130989, 620471833255971, 4211165312423001
Offset: 1
Keywords
Programs
-
Maxima
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);
Formula
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).
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)).
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.