A246458 Catalan number analogs for A048804, the generalized binomial coefficients for the radical sequence (A007947).

1, 1, 1, 5, 7, 7, 11, 143, 715, 2431, 4199, 29393, 52003, 37145, 7429, 215441, 392863, 4321493, 7960645, 58908773, 109402007, 407771117, 762354697, 3811773485, 35830670759, 19293438101, 327988447717, 2483341104143, 4709784852685, 17897182440203, 34062379482967

Offset: 0

Author

Tom Edgar, Aug 26 2014

Keywords

• nonn

Comments

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).

Examples

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

Links

• Tom Edgar and Michael Z. Spivey, Multiplicative functions, generalized binomial coefficients, and generalized Catalan numbers, Journal of Integer Sequences, Vol. 19 (2016), Article 16.1.6.

Crossrefs

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

Programs

Sage

[(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]]

Formula

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