%I #14 Jan 25 2016 14:25:04

%S 1,1,1,5,7,7,11,143,715,2431,4199,29393,52003,37145,7429,215441,

%T 392863,4321493,7960645,58908773,109402007,407771117,762354697,

%U 3811773485,35830670759,19293438101,327988447717,2483341104143,4709784852685,17897182440203,34062379482967

%N Catalan number analogs for A048804, the generalized binomial coefficients for the radical sequence (A007947).

%C One definition of the Catalan numbers is binomial(2*n,n) / (n+1); the current sequence models this definition using the generalized binomial coefficients arising from the radical sequence (A007947).

%H Tom Edgar and Michael Z. Spivey, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL19/Edgar/edgar3.html">Multiplicative functions, generalized binomial coefficients, and generalized Catalan numbers</a>, Journal of Integer Sequences, Vol. 19 (2016), Article 16.1.6.

%F a(n) = A048804(2n,n) / A007947(n+1).

%e A048804(10,5) = 42 and A007947(6) = 6, so a(5)=42/6=7.

%o (Sage)

%o [(1/(prod(x for x in prime_divisors(n+1))))*prod(prod(x for x in prime_divisors(i)) for i in [1..2*n])/prod(prod(x for x in prime_divisors(i)) for i in [1..n])^2 for n in [0..100]]

%Y Cf. A007947, A048804, A048803, A245798, A000108.

%K nonn

%O 0,4

%A _Tom Edgar_, Aug 26 2014