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 A307786 #12 May 08 2019 15:54:21 %S A307786 1,1,2,5,14,44,148,528,1972,7647,30605,125801,529131,2270481,9914870, %T A307786 43973755,197744417,900327160,4145285618,19280282194,90507546094, %U A307786 428476211848,2044274855774,9823314566417,47516954475991,231260870664189 %N A307786 Number of valid hook configurations of 312-avoiding permutations of [n]. %C A307786 The class of a Motzkin path is the set of indices i such that the i-th non-down step is an east step. For n > 0, a(n) is the number of pairs (P,Q) of Motzkin paths such that P and Q have the same class and P lies below or is equal to Q. %C A307786 Conjecture: This sequence is the binomial transform of A151347. %C A307786 The Defant article gives a functional equation that defines a generating function Q(x,y,z) such that Q(x,0,0) is the ordinary generating function of this sequence. %H A307786 Colin Defant, <a href="http://arxiv.org/abs/1904.10451">Motzkin intervals and valid hook configurations</a>, arXiv preprint arXiv:1904.10451 [math.CO], 2019. %H A307786 Wenjie Fang, <a href="http://arxiv.org/abs/1801.04809">A partial order on Motzkin paths</a>, arXiv preprint arXiv:1801.04809 [math.CO], 2018. %Y A307786 Appears to be the binomial transform of A151347. %K A307786 nonn %O A307786 0,3 %A A307786 _Colin Defant_, Apr 28 2019