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 A082490 #21 Aug 18 2025 11:13:39
%S A082490 0,1,2,0,2,3,1,2,4,0,1,2,0,3,4,2,3,5,1,2,3,1,3,4,2,3,6,0,1,2,0,2,3,1,
%T A082490 2,4,0,1,2,0,4,5,3,4,6,2,3,4,2,4,5,3,4,7,1,2,3,1,3,4,2,3,5,1,2,3,1,4,
%U A082490 5,3,4,6,2,3,4,2,4,5,3,4,8,0,1,2,0,2,3,1,2,4,0,1,2,0,3,4
%N A082490 Exponent of highest power of 3 dividing sum(0<=k<n, C(2n,n)).
%H A082490 Robert Israel, <a href="/A082490/b082490.txt">Table of n, a(n) for n = 1..10000</a>
%H A082490 J.-P. Allouche and J. Shallit, <a href="http://dx.doi.org/10.1016/S0304-3975(03)00090-2">The ring of k-regular sequences, II</a>, Theoret. Computer Sci., 307 (2003), 3-29.
%H A082490 J. Shallit, <a href="http://www.cs.uwaterloo.ca/~shallit/Talks/kreg7.ps">k-regular Sequences</a>
%H A082490 J. Shallit, <a href="http://www.math.uwaterloo.ca/~shallit/Papers/ntfl.ps">Number theory and formal languages</a>, in D. A. Hejhal, J. Friedman, M. C. Gutzwiller and A. M. Odlyzko, eds., Emerging Applications of Number Theory, IMA Volumes in Mathematics and Its Applications, V. 109, Springer-Verlag, 1999, pp. 547-570. (Example 1.)
%F A082490 a(n) = A007949(A006134(n)) = A007949 (n^2 * C(2n, n)) (Allouche, Shallit; Zagier) = 2*A007949(n) + A000989(n).
%p A082490 map(t -> padic:-ordp(t,3), ListTools:-PartialSums([seq(binomial(2*n,n),n=0..100)])); # _Robert Israel_, Mar 27 2018
%t A082490 IntegerExponent[#,3]&/@Accumulate[Table[Binomial[2n,n],{n,0,100}]]
%o A082490 (PARI) s=0; for(n=1, 150, s=s+binomial(2*n-2, n-1); print1(valuation(s, 3)", "))
%o A082490 (PARI) a(n) = valuation(n^2 * binomial(2*n, n), 3); \\ _Michel Marcus_, Mar 27 2018
%Y A082490 Cf. A000989, A006134, A007949.
%K A082490 nonn,hear
%O A082490 1,3
%A A082490 _Ralf Stephan_, Apr 28 2003