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A135322 a(n) = gcd(n!, binomial(2n,n)). 1

%I #21 Apr 03 2021 22:02:17

%S 1,1,2,2,2,12,12,24,90,20,4,168,28,1400,5400,720,90,5940,23100,46200,

%T 180180,17160,1560,140400,11700,45864,179928,13328,52360,5969040,

%U 397936,795872,3133746,12345060,726180,2863224,159068,318136,1255800,4958800

%N a(n) = gcd(n!, binomial(2n,n)).

%H G. C. Greubel, <a href="/A135322/b135322.txt">Table of n, a(n) for n = 0..1000</a>

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

%t Table[GCD[n!, Binomial[2n, n]], {n, 0, 60}] (* _Stefan Steinerberger_, Dec 07 2007 *)

%o (PARI) valp(n,p)=my(s); while(n\=p, s+=n); s

%o 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

%Y Cf. A000984, A263931.

%K nonn

%O 0,3

%A _Leroy Quet_, Dec 06 2007

%E More terms from _Stefan Steinerberger_, Dec 07 2007

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Last modified March 28 10:55 EDT 2024. Contains 371241 sequences. (Running on oeis4.)