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A246466 Catalan number analogs for A246465, the generalized binomial coefficients for A003557. 1
1, 1, 2, 1, 2, 6, 12, 3, 2, 2, 4, 2, 4, 20, 360, 45, 90, 30, 60, 30, 60, 60, 120, 90, 36, 252, 56, 28, 56, 56, 112, 7, 42, 42, 84, 14, 28, 28, 280, 70, 140, 3780, 7560, 3780, 2520, 2520, 5040, 630, 180, 36, 216, 108, 216, 24, 48, 12, 24, 24, 48, 72, 144, 1584 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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 sequence (A003557), which is n/rad(n).

LINKS

Table of n, a(n) for n=0..61.

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) = A246465(2n,n) / A003557(n+1).

EXAMPLE

A246465(14,7) = 12 and A003557(8) = 4, so a(7)=12/4=3.

PROG

(Sage)

D=[0]+[n/prod([x for x in prime_divisors(n)]) for n in [1..122]]

T=[[prod(D[1:m+1])/(prod(D[1:n+1])*prod(D[1:(m-n)+1])) for n in [0..m]] for m in [0..len(D)-1]]

[(1/D[i+1])*T[2*i][i] for i in [0..61]]

CROSSREFS

Cf. A003557, A246465, A245798, A000108, A007947, A246458.

Sequence in context: A110422 A131804 A254198 * A170829 A032085 A032163

Adjacent sequences:  A246463 A246464 A246465 * A246467 A246468 A246469

KEYWORD

nonn

AUTHOR

Tom Edgar, Aug 27 2014

STATUS

approved

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Last modified January 19 21:35 EST 2018. Contains 297938 sequences.