The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A108666 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A108666

Number of (1,1)-steps in all Delannoy paths of length n.
(history; published version)

#38 by Alois P. Heinz at Sat Apr 13 18:46:12 EDT 2024

STATUS

editing

approved

#37 by Alois P. Heinz at Sat Apr 13 18:46:02 EDT 2024

NAME

Number of (1, 1)-steps in all Delannoy paths of length n.

LINKS

G. C. Greubel, <a href="/A108666/b108666.txt">Table of n, a(n) for n = 0..1000</a> (terms 0..200 from Vincenzo Librandi)

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approved

editing

#36 by N. J. A. Sloane at Wed Mar 22 22:00:17 EDT 2023

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proposed

approved

#35 by Chai Wah Wu at Wed Mar 22 20:48:58 EDT 2023

STATUS

editing

proposed

#34 by Chai Wah Wu at Wed Mar 22 20:48:54 EDT 2023

PROG

(Python)

from math import comb

def A108666(n): return sum(comb(n, k)**2*k<<k-1 for k in range(1, n+1)) if n else 0 # Chai Wah Wu, Mar 22 2023

STATUS

approved

editing

#33 by R. J. Mathar at Mon May 25 05:07:20 EDT 2020

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editing

approved

#32 by R. J. Mathar at Mon May 25 05:07:16 EDT 2020

FORMULA

Recurrence: D-finite with recurrence (n-1)*(2*n-3)*a(n) = 4*(3*n^2-6*n+2)*a(n-1) - (n-1)*(2*n-1)*a(n-2). - Vaclav Kotesovec, Oct 18 2012

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approved

editing

#31 by N. J. A. Sloane at Mon Jan 20 12:55:25 EST 2020

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proposed

approved

#30 by Peter Luschny at Mon Jan 20 12:40:06 EST 2020

STATUS

editing

proposed

#29 by Peter Luschny at Mon Jan 20 12:30:36 EST 2020

CROSSREFS

a(n)/n = A047781(n) (for n >= 1).