A246466 Catalan number analogs for A246465, the generalized binomial coefficients for A003557.

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

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: A131804 A307519 A254198 * A170829 A032085 A032163

Adjacent sequences: A246463 A246464 A246465 * A246467 A246468 A246469

Keyword

nonn

Author

Tom Edgar, Aug 27 2014

Status

approved