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A246458 Catalan number analogs for A048804, the generalized binomial coefficients for the radical sequence (A007947). 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 11 14:03 EST 2017. Contains 295884 sequences.