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 A374835 #19 Jul 21 2024 12:48:25
%S A374835 0,1,0,4,14,72,370,1995,11064,62774,362614,2125479,12610410,75584363,
%T A374835 457000668,2783991972,17071362986,105287143740,652687596388,
%U A374835 4064618917998,25416557913498,159523021737403,1004594882114020,6345859437931884,40198433775513524
%N A374835 Number of ternary paths of length 3*n having exactly 1 hill.
%H A374835 Naiomi Cameron and J. E. McLeod, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL19/McLeod/mcleod3.html">Returns and Hills on Generalized Dyck Paths</a>, Journal of Integer Sequences, Vol. 19, 2016, #16.6.1.
%F A374835 a(n) = Sum_{k=0..n-1} (-1)^k * (k+1)*(k+2)/(2*n-k) * binomial(3*n-2-2*k,n-1-k).
%F A374835 G.f.: x * (g/(1 + x*g))^2, where g = 1 + x*g^3.
%o A374835 (PARI) a(n) = sum(k=0, n-1, (-1)^k*(k+1)*(k+2)/(2*n-k)*binomial(3*n-2-2*k, n-1-k));
%Y A374835 Column k=1 of A101371.
%Y A374835 Cf. A001764, A023053, A065601.
%K A374835 nonn
%O A374835 0,4
%A A374835 _Seiichi Manyama_, Jul 21 2024