A056201 -id:A056201 - cp's OEIS frontend

A056202 Central binomial coefficient A001405(n) divided by its characteristic cube divisor A056201(n).

1, 2, 3, 6, 10, 20, 35, 70, 126, 252, 462, 924, 1716, 429, 6435, 12870, 24310, 48620, 92378, 184756, 352716, 88179, 1352078, 2704156, 5200300, 1300075, 742900, 185725, 9694845, 155117520, 300540195, 601080390, 43214930, 86429860

Offset: 1

Labos Elemer, Aug 02 2000

nonn

			n=14, binomial(14,7) = 3432 and A056059(14) = 2, thus a(14) = 3432/(2*2*2) = 429.

Cf. A001405, A056056-A056060, A056201.

a(n) = A001405(n)/A056059(n)^3 = binomial(n, floor(n/2))/A056059(n)^3 = A001405(n)/A056201(n).

A056059 GCD of largest square and squarefree part of central binomial coefficients.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 3, 6, 2, 1, 1, 1, 3, 3, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 6, 3, 1, 1, 1, 2, 3, 6, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 2, 1, 1, 1, 1, 2, 3, 6, 6, 3, 1, 2, 2, 1, 2, 1, 3, 6, 1, 1, 1, 2, 1, 2

Offset: 1

Labos Elemer, Jul 26 2000

nonn

			n=14, binomial(14,7) = 3432 = 8*3*11*13. The largest square divisor is 4, squarefree part is 858. So a(14) = gcd(4,858) = 2.

Antti Karttunen, Table of n, a(n) for n = 1..10000

Cf. A000188, A001405, A007913, A008833, A034974, A046098, A055229, A055231.
Cf. A056056, A056057, A056058, A056060, A056061.
A056201 is the cube of this sequence.

Table[GCD[First@ Select[Reverse@ Divisors@ #, IntegerQ@ Sqrt@ # &], Times @@ Power @@@ Map[{#1, Mod[#2, 2]} & @@ # &, FactorInteger@ #]] &@ Binomial[n, Floor[n/2]], {n, 80}] (* Michael De Vlieger, Feb 18 2017, after Zak Seidov at A007913 *)

A001405(n) = binomial(n, n\2);
A055229(n) = { my(c=core(n)); gcd(c, n/c); } \\ Charles R Greathouse IV, Nov 20 2012
A056059(n) = A055229(A001405(n)); \\ Antti Karttunen, Jul 20 2017

from sympy import binomial, gcd
from sympy.ntheory.factor_ import core
def a001405(n): return binomial(n, n//2)
def a055229(n):
    c = core(n)
    return gcd(c, n//c)
def a(n): return a055229(a001405(n))
print([a(n) for n in range(1, 151)]) # Indranil Ghosh, Jul 20 2017

a(n) = A055229(A001405(n)), where A055229(n) = gcd(A008833(n), A007913(n)).

Formula clarified by Antti Karttunen, Jul 20 2017

cp's OEIS Frontend

A056202 Central binomial coefficient A001405(n) divided by its characteristic cube divisor A056201(n).

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A056059 GCD of largest square and squarefree part of central binomial coefficients.

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