A135322 a(n) = gcd(n!, binomial(2n,n)).

1, 1, 2, 2, 2, 12, 12, 24, 90, 20, 4, 168, 28, 1400, 5400, 720, 90, 5940, 23100, 46200, 180180, 17160, 1560, 140400, 11700, 45864, 179928, 13328, 52360, 5969040, 397936, 795872, 3133746, 12345060, 726180, 2863224, 159068, 318136, 1255800, 4958800

Offset: 0

Author

Leroy Quet, Dec 06 2007

Keywords

• nonn

Examples

			a(5) = 12 as gcd(5!, binomial(2*5, 5)) = gcd(120, 252) = 12. - _David A. Corneth_, Apr 03 2021
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000984, A263931.

Programs

Mathematica

Table[GCD[n!, Binomial[2n, n]], {n, 0, 60}] (* Stefan Steinerberger, Dec 07 2007 *)

PARI

valp(n,p)=my(s); while(n\=p, s+=n); s
a(n)=my(s=1,t); forprime(p=2,n, t=valp(n,p); t=min(t,valp(2*n,p)-2*t); if(t, s*=p^t)); s \\ Charles R Greathouse IV, Oct 09 2016

Extensions

More terms from Stefan Steinerberger, Dec 07 2007