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Revision History for A264772

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Showing entries 1-10 | older changes
Triangle T(n,k) = binomial(3*n - 2*k, 2*n - k), 0 <= k <= n.
(history; published version)
#30 by Amiram Eldar at Tue Feb 06 05:15:29 EST 2024
STATUS

reviewed

approved

#29 by Joerg Arndt at Tue Feb 06 03:40:49 EST 2024
STATUS

proposed

reviewed

#28 by Michel Marcus at Tue Feb 06 03:21:48 EST 2024
STATUS

editing

proposed

#27 by Michel Marcus at Tue Feb 06 03:21:44 EST 2024
LINKS

R. Sprugnoli, <a href="https://web.archive.org/web/20170401103408/http://www.dsi.unifi.it/~resp/Handbook.pdf">An Introduction to Mathematical Methods in Combinatorics, Section 5.6</a> , CreateSpace Independent Publishing Platform 2006, Section 5.6, ISBN-13: 978-1502925244.

#26 by Michel Marcus at Tue Feb 06 03:18:11 EST 2024
LINKS

P. Peter Bala, <a href="/A264772/a264772_1.pdf">A 4-parameter family of embedded Riordan arrays</a>

E. Lebensztayn, <a href="httphttps://www.dmtcsdoi.org/dmtcs-ojs/index10.php46298/dmtcs/article/view/1517.512">On the asymptotic enumeration of accessible automata, Section 2</a>, Discrete Mathematics and Theoretical Computer Science, Vol. 12, No.3, 2010, 75-80, Section 2.

R. Sprugnoli, <a href="http://www.dsi.unifi.it/~resp/Handbook.pdf">An Introduction to Mathematical Methods in Combinatorics, Section 5.6</a> CreateSpace Independent Publishing Platform 2006, ISBN-13: 978-1502925244.

FORMULA

O.g.f. : f(x)/(1 - t*x*g(x)), where f(x) = Sum_{n >= 0} binomial(3*n,n)*x^n and g(x) = Sum_{n >= 0} 1/(2*n + 1)*binomial(3*n,n)*x^n.

STATUS

approved

editing

#25 by Charles R Greathouse IV at Thu Sep 08 08:46:14 EDT 2022
PROG

(MAGMAMagma) /* As triangle */ [[Binomial(3*n-2*k, n-k): k in [0..n]]: n in [0.. 10]]; // Vincenzo Librandi, Dec 02 2015

Discussion
Thu Sep 08
08:46
OEIS Server: https://oeis.org/edit/global/2944
#24 by Susanna Cuyler at Mon Jul 22 17:27:54 EDT 2019
STATUS

proposed

approved

#23 by Michael De Vlieger at Mon Jul 22 16:46:20 EDT 2019
STATUS

editing

proposed

#22 by Michael De Vlieger at Mon Jul 22 16:46:17 EDT 2019
LINKS

Michael De Vlieger, <a href="/A264772/b264772.txt">Table of n, a(n) for n = 0..11475</a>

Paul Barry, <a href="https://arxiv.org/abs/1906.06373">On the halves of a Riordan array and their antecedents</a>, arXiv:1906.06373 [math.CO], 2019.

STATUS

approved

editing

#21 by Joerg Arndt at Fri Mar 02 11:48:33 EST 2018
STATUS

proposed

approved