A246466 - OEIS

%I #9 Jan 25 2016 14:24:36

%S 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,

%T 56,28,56,56,112,7,42,42,84,14,28,28,280,70,140,3780,7560,3780,2520,

%U 2520,5040,630,180,36,216,108,216,24,48,12,24,24,48,72,144,1584

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

%C 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).

%H Tom Edgar and Michael Z. Spivey, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL19/Edgar/edgar3.html">Multiplicative functions, generalized binomial coefficients, and generalized Catalan numbers</a>, Journal of Integer Sequences, Vol. 19 (2016), Article 16.1.6.

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

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

%o (Sage)

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

%o 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]]

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

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

%K nonn

%O 0,3

%A _Tom Edgar_, Aug 27 2014