%I #31 Jun 27 2023 11:01:17

%S 0,0,0,0,1,12,102,770,5545,39220,276144,1948212,13817680,98679990,

%T 710108396,5150076076,37641647410,277202062666,2056218941678,

%U 15358296210724,115469557503753,873561194459596,6647760790457218,50871527629923754,391345137795371013

%N Number of permutations in S_n containing exactly one increasing subsequence of length 4.

%H Brian Nakamura and Doron Zeilberger, <a href="/A217057/b217057.txt">Table of n, a(n) for n = 0..70</a>

%H Andrew R. Conway and Anthony J. Guttmann, <a href="https://arxiv.org/abs/2306.12682">Counting occurrences of patterns in permutations</a>, arXiv:2306.12682 [math.CO], 2023. See p. 16.

%H Brian Nakamura and Doron Zeilberger, <a href="http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/Gwilf.html">Using Noonan-Zeilberger Functional Equations to enumerate (in Polynomial Time!) Generalized Wilf classes</a>; <a href="/A217057/a217057.pdf">Local copy, pdf file only, no active links</a>

%H Brian Nakamura and Doron Zeilberger, <a href="https://arxiv.org/abs/1209.2353">Using Noonan-Zeilberger Functional Equations to enumerate (in Polynomial Time!) Generalized Wilf classes</a>, arXiv preprint arXiv:1209.2353, 2012.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Enumerations_of_specific_permutation_classes">Enumerations of specific permutation classes</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Subsequence">Subsequence</a>

%e a(4) = 1: 1234.

%e a(5) = 12: 12453, 12534, 13425, 13452, 14235, 15234, 23145, 23415, 23451, 31245, 41235, 51234.

%p # programs can be obtained from the Nakamura & Zeilberger link.

%Y Cf. A005802, A117158, A158005, A214015, A214152.

%K nonn

%O 0,6

%A _Alois P. Heinz_, Sep 25 2012