OFFSET
1,2
COMMENTS
Series reversion of x(1-x)/(1+x+2x^2).
Hankel transform is 4^C(n+1,2)=A053763(n+1).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..200
FORMULA
a(n)=sum{k=0..n, sum{j=0..n, C(n,j)*C(n-k,j+k-n)*C(n-k)*3^(j+k-n)}}, C(n)=A000108(n); a(n)=(1/(2*pi))*int(x^n*sqrt(7+6*x-x^2)/(2+x),x,-1,7);
D-finite with recurrence: n*a(n) = (4*n-9)*a(n-1) + (19*n-39)*a(n-2) + 14*(n-3)*a(n-3) . - Vaclav Kotesovec, Oct 20 2012
a(n) ~ 7^(n+1/2)/(9*sqrt(2*Pi)*n^(3/2)) . - Vaclav Kotesovec, Oct 20 2012
MATHEMATICA
Rest[CoefficientList[Series[(1-x-Sqrt[1-6*x-7*x^2])/(2*(1+2*x)), {x, 0, 20}], x]] (* Vaclav Kotesovec, Oct 20 2012 *)
Table[(1/(2*Pi))*Integrate[x^n*Sqrt[7+6*x-x^2]/(2+x), {x, -1, 7}], {n, 0, 10}] (* Vaclav Kotesovec, Oct 20 2012 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Apr 01 2007
EXTENSIONS
Offset corrected to 1, Vaclav Kotesovec, Oct 20 2012
STATUS
approved