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

Author

Tom Edgar, Aug 27 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 sequence (A003557), which is n/rad(n).

Examples

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

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

Programs

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]]

Formula

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