OFFSET
0,2
COMMENTS
Apply the Riordan matrix ((1+sqrt(1-4x))/2,(1-sqrt(1-4x))/2) (inverse of (1/(1-x),x(1-x))) to 5^n.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
FORMULA
a(n) = 0^n + sum{k=0..n, 4^(k+1)*C(2n-1, n-k-1)*2*(k+1)/(n+k+1)}
D-finite with recurrence: 4*n*a(n) = (41*n-24)*a(n-1) - 50*(2*n-3)*a(n-2). - Vaclav Kotesovec, Oct 17 2012
a(n) ~ 3*5^(2*n-1)/4^n. - Vaclav Kotesovec, Oct 17 2012
MATHEMATICA
CoefficientList[Series[(1+Sqrt[1-4*x])/(5*Sqrt[1-4*x]-3), {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 17 2012 *)
PROG
(PARI) x='x+O('x^66); Vec((1+sqrt(1-4*x))/(5*sqrt(1-4*x)-3)) \\ Joerg Arndt, May 13 2013
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Mar 12 2005
STATUS
approved