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

0,4

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).

Links

Table of n, a(n) for n=0..30.

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.

Formula

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

Example

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

Prog

(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]]

Crossrefs

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

Sequence in context: A216835 A033932 A144186 * A153979 A126992 A028316

Adjacent sequences: A246455 A246456 A246457 * A246459 A246460 A246461

Keyword

nonn

Author

Tom Edgar, Aug 26 2014

Status

approved