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 A023826 #23 Jun 12 2025 08:08:31
%S A023826 0,2,3,4,5,7,6,9,9,10,10,9,9,13,14,14,14,15,15,15,16,19,16,19,18,21,
%T A023826 20,18,19,21,21,22,22,23,25,24,24,27,26,28,26,30,28,28,29,28,28,30,30,
%U A023826 31,31,31,31,35,30,31,31,32,34,33,33,38,39,39,37,39,38,39,40,43,40,41,41,44,44,43,44,46,45
%N A023826 Sum of exponents in prime-power factorization of C(4n,n).
%C A023826 Also sum of exponents of primes in multinomial coefficient M(4n; n,n,n,n)/M(3n; n,n,n).
%H A023826 Ivan Neretin, <a href="/A023826/b023826.txt">Table of n, a(n) for n = 0..10000</a>
%F A023826 From _Amiram Eldar_, Jun 11 2025: (Start)
%F A023826 a(n) = A001222(A005810(n)).
%F A023826 a(n) = A022559(4*n) - A022559(3*n) - A022559(n). (End)
%p A023826 with(numtheory):a:=proc(n) if n=0 then 0 else bigomega(binomial(4*n,n)) fi end: seq(a(n), n=0..78); # _Zerinvary Lajos_, Apr 11 2008
%t A023826 Join[{0}, Table[Total[FactorInteger[Binomial[4 n, n]][[All, 2]]], {n, 78}]] (* _Ivan Neretin_, Nov 02 2017 *)
%o A023826 (PARI) a(n) = bigomega(binomial(4*n, n)); \\ _Amiram Eldar_, Jun 11 2025
%Y A023826 Cf. A001222, A005810, A022559.
%K A023826 nonn
%O A023826 0,2
%A A023826 _Clark Kimberling_
%E A023826 Offset changed to 0 and a(0) prepended by _Amiram Eldar_, Jun 11 2025