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 A318407 #17 Sep 17 2018 03:41:49
%S A318407 0,1,1,1,1,1,2,1,4,1,1,1,5,3,1,1,7,8,3,3,1,8,13,6,4,1,10,23,16,13,6,1,
%T A318407 1,11,31,29,19,10,1,1,13,46,59,46,39,13,5,1,14,57,90,75,58,23,6,1,16,
%U A318407 77,153,158,147,97,39,15,1,1,17,91,210,248,222,155,62,21,1
%N A318407 Triangle read by rows: T(n,k) is the number of Markov equivalence classes whose skeleton is the caterpillar graph on n nodes that contain precisely k immoralities.
%C A318407 The n-th row of the triangle T(n,k) is the coefficient sequence of a generating polynomial admitting a recursive formula given in Theorem 4.3 of the paper by A. Radhakrishnan et al. below.
%C A318407 The sum of the entries in the n-th row is A318406(n).
%C A318407 The entries in the n-th row appear to alway form a unimodal sequence.
%H A318407 A. Radhakrishnan, L. Solus, and C. Uhler. <a href="https://arxiv.org/abs/1706.06091">Counting Markov equivalence classes for DAG models on trees</a>, arXiv:1706.06091 [math.CO], 2017; Discrete Applied Mathematics 244 (2018): 170-185.
%F A318407 A recursion whose n-th iteration is a polynomial with coefficient vector the n-th row of T(n,k):
%F A318407 W_0 = 0
%F A318407 W_1 = 1
%F A318407 W_2 = 1
%F A318407 W_3 = 1 + x
%F A318407 W_4 = 1 + 2*x
%F A318407 for n>4:
%F A318407 if n is even:
%F A318407 W_n = W_{n-1} + x*W_{n-2}
%F A318407 if n is odd:
%F A318407 W_n = (x + 2)*W_{n-2} + (x^3 - x^2 + x-2)*W_{n-3} + (x^2 + 1)*W_{n-4}
%F A318407 (see Theorem 4.3 of Radhakrishnan et al. for proof.)
%e A318407 The triangle T(n,k) begins:
%e A318407 n\k| 0 1 2 3 4 5 6 7 8 9
%e A318407 -----+------------------------------------------------
%e A318407 0 | 0
%e A318407 1 | 1
%e A318407 2 | 1
%e A318407 3 | 1 1
%e A318407 4 | 1 2
%e A318407 5 | 1 4 1 1
%e A318407 6 | 1 5 3 1
%e A318407 7 | 1 7 8 3 3
%e A318407 8 | 1 8 13 6 4
%e A318407 9 | 1 10 23 16 13 6 1
%e A318407 10 | 1 11 31 29 19 10 1
%e A318407 11 | 1 13 46 59 46 39 13 5
%e A318407 12 | 1 14 57 90 75 58 23 6
%e A318407 13 | 1 16 77 153 158 147 97 39 15 1
%e A318407 14 | 1 17 91 210 248 222 155 62 21 1
%t A318407 W[0] = 0; W[1] = 1; W[2] = 1; W[3] = 1 + x; W[4] = 1 + 2x;
%t A318407 W[n_] := W[n] = If[EvenQ[n], W[n-1] + x W[n-2], (x+2) W[n-2] + (x^3 - x^2 + x - 2) W[n-3] + (x^2 + 1) W[n-4]];
%t A318407 Join[{0}, Table[CoefficientList[W[n], x], {n, 0, 14}]] // Flatten (* _Jean-François Alcover_, Sep 17 2018 *)
%o A318407 (PARI) pol(n) = if (n==0, 0, if (n==1, 1, if (n==2, 1, if (n==3, 1 + x, if (n==4, 1 + 2*x, if (n%2, (x + 2)*pol(n-2) + (x^3 - x^2 + x-2)*pol(n-3) + (x^2 + 1)*pol(n-4), pol(n-1) + x*pol(n-2)))))));
%o A318407 row(n) = Vecrev(pol(n)); \\ _Michel Marcus_, Sep 04 2018
%Y A318407 Cf. A007984, A318406.
%K A318407 nonn,tabf,easy
%O A318407 0,7
%A A318407 _Liam Solus_, Aug 26 2018