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 A023821 #17 Jun 12 2025 08:12:23
%S A023821 0,2,3,3,6,5,6,8,8,9,11,9,10,10,12,11,12,13,13,14,17,15,17,17,16,18,
%T A023821 19,17,20,17,19,21,19,19,22,20,20,21,22,21,23,26,26,28,29,25,29,28,27,
%U A023821 28,29,26,32,31,31,32,30,31,33,33,31,31,35,33,32,30,31,32,36,32,35,34,33,38,37,35,38,35
%N A023821 Sum of exponents in prime-power factorization of C(3n,n-2).
%H A023821 Ivan Neretin, <a href="/A023821/b023821.txt">Table of n, a(n) for n = 2..10000</a>
%F A023821 From _Amiram Eldar_, Jun 12 2025: (Start)
%F A023821 a(n) = A001222(A003408(n-2)).
%F A023821 a(n) = A023820(n) - A001222(2*n+2) + A001222(n-1). (End)
%t A023821 Join[{0},Table[Total[Transpose[FactorInteger[Binomial[3n,n-2]]][[2]]],{n,3,80}]] (* _Harvey P. Dale_, Sep 23 2014 *)
%t A023821 a[n_] := PrimeOmega[Binomial[3*n, n-2]]; Array[a, 100, 2] (* _Amiram Eldar_, Jun 12 2025 *)
%o A023821 (PARI) a(n) = bigomega(binomial(3*n, n-2)); \\ _Amiram Eldar_, Jun 12 2025
%Y A023821 Cf. A001222, A003408, A023819, A023820, A023822, A023823, A023824, A023825..
%K A023821 nonn
%O A023821 2,2
%A A023821 _Clark Kimberling_