OFFSET
0,2
FORMULA
From Vaclav Kotesovec, Jun 12 2013: (Start)
G.f.: 1/((1-5*x)*sqrt(1-4*x)).
Recurrence: n*a(n) = (9*n-2)*a(n-1) - 10*(2*n-1)*a(n-2).
a(n) ~ 5^(n+1/2). (End)
a(n) = 5^(n+1/2) - 2^(n+1)*(2*n+1)!!*hypergeom([1,n+3/2], [n+2], 4/5)/(5*(n+1)!). - Vladimir Reshetnikov, Oct 14 2016
MATHEMATICA
Table[5^n Sum[Binomial[2k, k]/5^k, {k, 0, n}], {n, 0, 30}] (* Harvey P. Dale, Aug 08 2011 *)
Round@Table[5^(n + 1/2) - 2^(n + 1) (2 n + 1)!! Hypergeometric2F1[1, n + 3/2, n + 2, 4/5]/(5 (n + 1)!), {n, 0, 20}] (* Round is equivalent to FullSimplify here, but is much faster - Vladimir Reshetnikov, Oct 14 2016 *)
PROG
(PARI) a(n) = 5^n*sum(k=0, n, binomial(2*k, k)/5^k); \\ Michel Marcus, Oct 14 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jan 21 2009
STATUS
approved