OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..300
FORMULA
G.f.: ((1+x-sqrt(1-6*x+x^2))/(4*x))^5.
a(n)= (5/n)*Sum_{k=1,..,n} binomial(n,k)*binomial(n+k+4,k-1), a(0)=1.
a(n) = 5*hypergeom([1-n, n+6], [2], -1), n>=1, a(0)=1.
Recurrence: n*(n+5)*a(n) = n*(7*n+23)*a(n-1) - (n+2)*(7*n-9)*a(n-2) + (n-3)*(n+2)*a(n-3). - Vaclav Kotesovec, Oct 18 2012
a(n) ~ 5*sqrt(3*sqrt(2)-4)*(17-12*sqrt(2)) * (3+2*sqrt(2))^(n+5)/(16*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 18 2012
MATHEMATICA
CoefficientList[Series[((1+x-Sqrt[1-6*x+x^2])/(4*x))^5, {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 18 2012 *)
PROG
(PARI) x='x+O('x^50); Vec(((1+x-sqrt(1-6*x+x^2))/(4*x))^5) \\ G. C. Greubel, Mar 16 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Sep 12 2005
STATUS
approved