A327703 a(n) = (binomial(n,floor(n/2)))/(greatest common divisor of all numbers in n-th row of Pascal's triangle excluding 1 and n).

1, 1, 4, 5, 5, 21, 84, 42, 84, 132, 264, 6435, 6435, 715, 2860, 4862, 9724, 352716, 705432, 58786, 117572, 1040060, 2080120, 6686100, 13372200, 2674440, 5348880, 9694845, 9694845, 583401555

Offset

4,3

Comments

For all values of a(n), where a(n) is not equal to A001405(n), n is either: a prime, a power of a prime, a prime +1 or a power of a prime +1.

Links

Table of n, a(n) for n=4..33.

Formula

a(n) = A001405(n)/A328202(n).

Example

For n = 17, a(17) = A001405(17)/A328202(17) = 24310/34 = 715.

Mathematica

a[n_] := Binomial[n, Floor[n/2]]/GCD @@ Binomial[n, Range[2, n/2]]; Array[a, 30, 4] (* Amiram Eldar, Oct 24 2019 *)

Prog

(PARI) a(n) = binomial(n, n\2)/gcd(vector((n+1)\2-1, k, binomial(n, k+1))); \\ Michel Marcus, Oct 24 2019

Crossrefs

Cf. A001405, A328202.

Sequence in context: A154914 A154916 A344024 * A077061 A072508 A075566

Adjacent sequences: A327700 A327701 A327702 * A327704 A327705 A327706

Keyword

nonn

Author

Joel Kaufmann, Oct 24 2019

Status

approved