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

1,2

Links

Table of n, a(n) for n=1..21.

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.

Prog

(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);

Crossrefs

Sequence in context: A284717 A027277 A242798 * A234282 A366011 A365250

Adjacent sequences: A239195 A239196 A239197 * A239199 A239200 A239201

Keyword

nonn

Author

Vladimir Kruchinin, Mar 12 2014

Status

approved