The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A104562

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A104562

Inverse of the Motzkin triangle A064189.
(history; published version)

#71 by Alois P. Heinz at Sun Sep 01 18:27:29 EDT 2024

STATUS

reviewed

approved

#70 by Andrew Howroyd at Sun Sep 01 17:25:40 EDT 2024

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proposed

reviewed

#69 by Michel Marcus at Sun Sep 01 17:23:54 EDT 2024

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editing

proposed

#68 by Michel Marcus at Sun Sep 01 17:23:50 EDT 2024

LINKS

Gross, Jonathan L. ; Gross, Toufik Mansour, Toufik; Tucker, Thomas W.; Wang, Tucker, and David G. L. Wang, <a href="https://doi.org/10.1016/j.jmaa.2016.04.033">Root geometry of polynomial sequences. II: Type (1,0)</a>, J. Math. Anal. Appl. 441, No. 2, 499-528 (2016).

A. Luzón, D. Merlini, M. A. Morón, and R. Sprugnoli, <a href="http://dx.doi.org/10.1016/j.dam.2014.03.005">Complementary Riordan arrays</a>, Discrete Applied Mathematics, 172 (2014) 75-87.

EXAMPLE

[0] 1;

[1] -1, 1;

[2] 0, -2, 1;

[3] 1, 1, -3, 1;

[4] -1, 2, 3, -4, 1;

[5] 0, -4, 2, 6, -5, 1;

[6] 1, 2, -9, 0, 10, -6, 1;

[7] -1, 3, 9, -15, -5, 15, -7, 1;

[8] 0, -6, 3, 24, -20, -14, 21, -8, 1;

[9] 1, 3, -18, -6, 49, -21, -28, 28, -9, 1.

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...

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reviewed

editing

#67 by Andrew Howroyd at Sun Sep 01 17:15:08 EDT 2024

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proposed

reviewed

#66 by Jason Yuen at Sun Sep 01 17:00:49 EDT 2024

STATUS

editing

proposed

#65 by Jason Yuen at Sun Sep 01 17:00:36 EDT 2024

FORMULA

T(n, k) = (-1)^(n - k)*C(n, k)*hypergeom([(k - n)/2, (k - n + 1)/2], [-n], 4)) for n >= 1. - Peter Luschny, Apr 25 2016

STATUS

approved

editing

#64 by Alois P. Heinz at Wed Feb 15 10:50:00 EST 2023

STATUS

editing

approved

#63 by Alois P. Heinz at Wed Feb 15 10:49:56 EST 2023

DATA

1, -1, 1, 0, -2, 1, 1, 1, -3, 1, -1, 2, 3, -4, 1, 0, -4, 2, 6, -5, 1, 1, 2, -9, 0, 10, -6, 1, -1, 3, 9, -15, -5, 15, -7, 1, 0, -6, 3, 24, -20, -14, 21, -8, 1, 1, 3, -18, -6, 49, -21, -28, 28, -9, 1, -1, 4, 18, -36, -35, 84, -14, -48, 36, -10, 1, 0, -8, 4, 60, -50, -98, 126, 6, -75, 45, -11, 1, 1, 4, -30, -20, 145, -36, -210, 168, 45, -110, 55, -12, 1

STATUS

approved

editing

#62 by Alois P. Heinz at Wed Feb 15 10:47:54 EST 2023

STATUS

proposed

approved