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 A334772 #10 Jan 11 2021 13:22:55
%S A334772 2,12,66,36,576,1168,80,2610,17376,16220,150,8520,129800,448800,
%T A334772 202416,252,22680,659560,5748750,10861056,2395540,392,52416,2596608,
%U A334772 46412200,241987500,253940736,27517568,576,109116,8505728,273322980,3121135440,9885006250,5807161344,310123764
%N A334772 Array read by antidiagonals: T(n,k) is the number of permutations of k indistinguishable copies of 1..n arranged in a circle with exactly 2 local maxima.
%C A334772 T(n,k) is divisible by n and 2*T(n,k) is divisible by n*k.
%H A334772 Andrew Howroyd, <a href="/A334772/b334772.txt">Table of n, a(n) for n = 2..1276</a>
%F A334772 T(n,k) = n*k*( P(k,4)^(n-2) * P(k-2,2)^2 + 4*(Sum_{j=0..n-3} P(k-1,3) * P(k-2,2) * P(k,2)^j * P(k, 4)^(n-j-3)) + 4*(Sum_{j=0..n-4} (j + 1) * P(k-1,3)^2 * P(k,2)^j * P(k,4)^(n-j-4)) )/2 where P(n,k) = binomial(n+k-1, k-1).
%F A334772 T(n,k) = n*k*( (k^2 + 4*k + 1)^2*binomial(k+3, 3)^(n-2) + 12*(k + 2)*(k+1)^(n-2) - 6*k*(k+5)*n*(k+1)^(n-2))/(2*(k + 5)^2).
%e A334772 Array begins:
%e A334772 ==========================================================
%e A334772 n\k | 2 3 4 5
%e A334772 ----|----------------------------------------------------
%e A334772 2 | 2 12 36 80 ...
%e A334772 3 | 66 576 2610 8520 ...
%e A334772 4 | 1168 17376 129800 659560 ...
%e A334772 5 | 16220 448800 5748750 46412200 ...
%e A334772 6 | 202416 10861056 241987500 3121135440 ...
%e A334772 7 | 2395540 253940736 9885006250 203933233280 ...
%e A334772 8 | 27517568 5807161344 395426250000 13051880894720 ...
%e A334772 ...
%e A334772 The T(2,3) = 12 permutations of 111222 with 2 local maxima are 112122, 112212 and their rotations.
%e A334772 The T(3,2) = 66 permutations of 112233 with 2 local maxima are 112323, 113223, 113232, 121233, 121332, 122133, 122313, 123213, 123123, 123132, 131322 and their rotations.
%o A334772 (PARI) T(n,k)={n*k*( (k^2 + 4*k + 1)^2*binomial(k+3,3)^(n-2) + 12*(k + 2)*(k+1)^(n-2) - 6*k*(k+5)*n*(k+1)^(n-2))/(2*(k + 5)^2)}
%Y A334772 Columns k=2..6 are A159716, A159722, A159728, A159734, A159737.
%Y A334772 Cf. A334773, A334774, A334778.
%K A334772 nonn,tabl
%O A334772 2,1
%A A334772 _Andrew Howroyd_, May 10 2020