The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A128088

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A128088

a(n) = Sum_{k=0..n} A000108(k)*A001263(n+1,k+1), where A000108 is the Catalan numbers and A001263 is the Narayana triangle.
(history; published version)

#28 by Peter Luschny at Mon Nov 06 08:34:33 EST 2023

STATUS

reviewed

approved

#27 by Joerg Arndt at Mon Nov 06 08:27:58 EST 2023

STATUS

proposed

reviewed

#26 by Michel Marcus at Mon Nov 06 08:25:45 EST 2023

STATUS

editing

proposed

#25 by Michel Marcus at Mon Nov 06 08:25:40 EST 2023

LINKS

Alice L. L. Gao, and Sergey Kitaev, <a href="https://arxiv.org/abs/1903.08946">On partially ordered patterns of length 4 and 5 in permutations</a>, arXiv:1903.08946 [math.CO], 2019.

Alice L. L. Gao, and Sergey Kitaev, <a href="https://doi.org/10.37236/8605">On partially ordered patterns of length 4 and 5 in permutations</a>, The Electronic Journal of Combinatorics 26(3) (2019), P3.26.

STATUS

proposed

editing

#24 by Peter Luschny at Mon Nov 06 07:59:18 EST 2023

STATUS

editing

proposed

#23 by Peter Luschny at Mon Nov 06 07:58:11 EST 2023

FORMULA

a(n) = hypergeom([1/2, -n - 1, -n], [2, 2], 4). - Vaclav Kotesovec, May 14 2016

MAPLE

a := n -> hypergeom([1/2, -n - 1, -n], [2, 2], 4):

seq(simplify(a(n)), n = 0..23); # Peter Luschny, Nov 06 2023

STATUS

approved

editing

Discussion

Mon Nov 06

07:59

Peter Luschny: Formula of Vaclav lifted from MMA to formula section.

#22 by Alois P. Heinz at Sun Dec 13 09:49:50 EST 2020

STATUS

editing

approved

#21 by Alois P. Heinz at Sun Dec 13 09:49:22 EST 2020

DATA

1, 2, 6, 24, 115, 618, 3591, 22088, 141903, 943590, 6452490, 45159480, 322305165, 2339100078, 17223121350, 128428689888, 968383277791, 7374380672718, 56655414930642, 438741242896680, 3422125459579869, 26866961380274598, 212191772351034249, 1685036376746788392

STATUS

proposed

editing

#20 by Sergey Kitaev at Sun Dec 13 06:55:46 EST 2020

STATUS

editing

proposed

#19 by Sergey Kitaev at Sun Dec 13 04:59:19 EST 2020

COMMENTS

a(n) is the number of permutations of length n+1 avoiding the partially ordered pattern (POP) {1>2>3>4} of length 5. That is, the number of length n+1 permutations having no subsequences of length 5 in which the element in position 1 is larger than the element in position 2, which in turn is larger than the element in position 3, and that element is larger than the element in position 4. - Sergey Kitaev, Dec 13 2020

LINKS

Alice L. L. Gao, Sergey Kitaev, <a href="https://doi.org/10.37236/8605">On partially ordered patterns of length 4 and 5 in permutations</a>, The Electronic Journal of Combinatorics 26(3) (2019), P3.26.

STATUS

approved

editing