The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A026940

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A026940

a(n) = Sum_{k=0..n-1} T(n,k) * T(n,k+1), with T given by A026300.
(history; published version)

#35 by Michael De Vlieger at Tue Aug 06 00:03:00 EDT 2024

STATUS

reviewed

approved

#34 by Andrew Howroyd at Mon Aug 05 22:41:57 EDT 2024

STATUS

proposed

reviewed

#33 by Jason Yuen at Mon Aug 05 22:09:06 EDT 2024

STATUS

editing

proposed

#32 by Jason Yuen at Mon Aug 05 22:09:02 EDT 2024

FORMULA

a(n) = Sum_{k=0..n} binomial(2*n, 2*k+1)*binomial(2*k+1, k)/(k+2)), , see Amdeberhan link. - Michel Marcus, Jul 29 2015

STATUS

approved

editing

#31 by Michel Marcus at Tue Sep 06 02:56:31 EDT 2022

STATUS

reviewed

approved

#30 by Joerg Arndt at Tue Sep 06 02:47:11 EDT 2022

STATUS

proposed

reviewed

#29 by Peter Luschny at Mon Sep 05 13:51:28 EDT 2022

STATUS

editing

proposed

#28 by Peter Luschny at Mon Sep 05 13:49:21 EDT 2022

FORMULA

a(n) = n*hypergeom([1/2 - n, 1 - n], [3], 4). - Jean-François Alcover, Sep 22 2018

MAPLE

a := n -> n*hypergeom([1/2 - n, 1 - n], [3], 4);

seq(simplify(a(n)), n = 1..22); # Peter Luschny, Sep 05 2022

STATUS

proposed

editing

Discussion

Mon Sep 05

13:51

Peter Luschny: I added Jean-François's formula from the Mma program to the formula section.

#27 by Michel Marcus at Mon Sep 05 13:07:45 EDT 2022

STATUS

editing

proposed

#26 by Michel Marcus at Mon Sep 05 13:07:26 EDT 2022

LINKS

Tewodros Amdeberhan, Moa Apagodu, and Doron Zeilberger, <a href="http://arxiv.org/abs/1507.07660">Wilf's "Snake Oil" Method Proves an Identity in The Motzkin Triangle</a>, arXiv:1507.07660 [math.CO], 2015.

Discussion

Mon Sep 05

13:07

Michel Marcus: should use ~~~~ to sign