The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A081277 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A081277

Square array of unsigned coefficients of Chebyshev polynomials of the first kind.
(history; published version)

#35 by Peter Luschny at Tue Jul 26 16:29:41 EDT 2022

STATUS

editing

approved

#34 by Peter Luschny at Tue Jul 26 16:27:20 EDT 2022

CROSSREFS

Cf. A053120 (antidiagonals give signed version) and A124182 (skewed version) . - Mathias Zechmeister, Jul 26 2022

STATUS

proposed

editing

Discussion

Tue Jul 26

16:29

Peter Luschny: ... because A053120 defined as a triangle. By the way, almost everyline in the OEIS ends with a period.

#33 by Mathias Zechmeister at Tue Jul 26 16:15:04 EDT 2022

STATUS

editing

proposed

#32 by Mathias Zechmeister at Tue Jul 26 16:14:51 EDT 2022

CROSSREFS

Cf. A053120 (signed version) and A124182 (skewed version) - Mathias Zechmeister, Jul 26 2022

STATUS

approved

editing

#31 by Michel Marcus at Sun Feb 13 04:31:52 EST 2022

STATUS

reviewed

approved

#30 by Joerg Arndt at Sun Feb 13 04:17:15 EST 2022

STATUS

proposed

reviewed

#29 by Jon E. Schoenfield at Sun Feb 13 04:13:14 EST 2022

STATUS

editing

proposed

#28 by Jon E. Schoenfield at Sun Feb 13 04:13:09 EST 2022

FORMULA

T(n, k) = (n+2k)C*binomial(n+k-1, k-1)*2^(n-1)/k, k > 0.

T(n, 0) defined by Gg.f. (1-x)/(1-2x). Other rows are defined by (1-x)/(1-2x)^n.

T(n, 0) = 0 if n < 0, T(0, k) = 0 if k < 0, T(0, 0) = T(1, 0) = 1, T(n, k) = T(n, k-1) + 2*T(n-1, k); for example, 160 = 48 + 2*56 for n = 4 and k = 2. -Philippe Deléham, Aug 12 2005

EXAMPLE

1, 1, 2, 4, 8, ...

1, 3, 8, 20, 48, ...

1, 5, 18, 56, 160, ...

1, 7, 32, 120, 400, ...

1, 9, 50, 220, 840, ...

...

1;

1..., 1;

1..., 3..., 2;

1..., 5..., 8..., 4;

1..., 7..., 18.., 20..., 8;

STATUS

approved

editing

#27 by Susanna Cuyler at Fri Apr 24 21:00:58 EDT 2020

STATUS

proposed

approved

#26 by Michel Marcus at Fri Apr 24 16:48:24 EDT 2020

STATUS

editing

proposed