This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A023819 #22 Jun 12 2025 08:08:56
%S A023819 0,1,2,4,4,4,6,8,6,7,8,11,11,11,11,12,10,12,11,15,13,13,18,18,17,16,
%T A023819 17,19,17,18,19,22,18,18,20,21,19,21,22,23,22,21,23,28,27,27,28,30,27,
%U A023819 28,26,28,29,28,31,32,29,31,31,35,32,33,35,34,31,30,31,34,31,32,35,36,33,34,35,38,37,36,36
%N A023819 Sum of exponents in prime-power factorization of C(3n,n).
%C A023819 Equivalently, sum of exponents of primes in multinomial coefficient M(3n; n,n,n)/C(2n,n).
%H A023819 Ivan Neretin, <a href="/A023819/b023819.txt">Table of n, a(n) for n = 0..10000</a>
%F A023819 From _Amiram Eldar_, Jun 11 2025: (Start)
%F A023819 a(n) = A001222(A005809(n)).
%F A023819 a(n) = A022559(3*n) - A022559(2*n) - A022559(n). (End)
%p A023819 with(numtheory):(combinat):a:=proc(n) if n=0 then 0 else bigomega(binomial(3*n,n)) fi end: seq(a(n), n=0..78); # _Zerinvary Lajos_, Apr 11 2008
%t A023819 Join[{0}, Table[Total[FactorInteger[Binomial[3 n, n]][[All, 2]]], {n, 78}]] (* _Ivan Neretin_, Nov 02 2017 *)
%o A023819 (PARI) a(n) = bigomega(binomial(3*n, n)); \\ _Amiram Eldar_, Jun 11 2025
%Y A023819 Cf. A001222, A005809, A022559.
%K A023819 nonn
%O A023819 0,3
%A A023819 _Clark Kimberling_
%E A023819 Edited by _N. J. A. Sloane_ at the suggestion of _R. J. Mathar_, May 31 2008
%E A023819 Offset changed to 0 and a(0) prepended by _Amiram Eldar_, Jun 11 2025