A217057 Number of permutations in S_n containing exactly one increasing subsequence of length 4.

0, 0, 0, 0, 1, 12, 102, 770, 5545, 39220, 276144, 1948212, 13817680, 98679990, 710108396, 5150076076, 37641647410, 277202062666, 2056218941678, 15358296210724, 115469557503753, 873561194459596, 6647760790457218, 50871527629923754, 391345137795371013

Offset: 0

Author

Alois P. Heinz, Sep 25 2012

Keywords

• nonn

Examples

			a(4) = 1: 1234.
a(5) = 12: 12453, 12534, 13425, 13452, 14235, 15234, 23145, 23415, 23451, 31245, 41235, 51234.
		

Links

• Brian Nakamura and Doron Zeilberger, Table of n, a(n) for n = 0..70
• Andrew R. Conway and Anthony J. Guttmann, Counting occurrences of patterns in permutations, arXiv:2306.12682 [math.CO], 2023. See p. 16.
• Brian Nakamura and Doron Zeilberger, Using Noonan-Zeilberger Functional Equations to enumerate (in Polynomial Time!) Generalized Wilf classes; Local copy, pdf file only, no active links
• Brian Nakamura and Doron Zeilberger, Using Noonan-Zeilberger Functional Equations to enumerate (in Polynomial Time!) Generalized Wilf classes, arXiv preprint arXiv:1209.2353, 2012.
• Wikipedia, Enumerations of specific permutation classes
• Wikipedia, Subsequence

Crossrefs

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

Programs

Maple

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