A023826 - OEIS

%I #13 Nov 02 2017 18:05:19

%S 2,3,4,5,7,6,9,9,10,10,9,9,13,14,14,14,15,15,15,16,19,16,19,18,21,20,

%T 18,19,21,21,22,22,23,25,24,24,27,26,28,26,30,28,28,29,28,28,30,30,31,

%U 31,31,31,35,30,31,31,32,34,33,33,38,39,39,37,39,38,39,40,43,40,41,41,44,44,43,44,46,45

%N Sum of exponents in prime-power factorization of C(4n,n).

%C Also sum of exponents of primes in multinomial coefficient M(4n; n,n,n,n)/M(3n; n,n,n).

%H Ivan Neretin, <a href="/A023826/b023826.txt">Table of n, a(n) for n = 1..10000</a>

%p with(numtheory):a:=proc(n) if n=0 then 0 else bigomega(binomial(4*n,n)) fi end: seq(a(n), n=1..78); # _Zerinvary Lajos_, Apr 11 2008

%t Table[Total[FactorInteger[Binomial[4 n, n]][[All, 2]]], {n, 78}] (* _Ivan Neretin_, Nov 02 2017 *)

%K nonn

%O 1,1

%A _Clark Kimberling_