The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A163841 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A163841

Triangle interpolating the swinging factorial (A056040) restricted to even indices with its binomial transform. Same as interpolating bilateral Schroeder paths (A026375) with the central binomial coefficients (A000984).
(history; published version)

#21 by Peter Luschny at Fri May 08 17:41:21 EDT 2020

STATUS

editing

approved

#20 by Peter Luschny at Fri May 08 17:41:14 EDT 2020

REFERENCES

Peter Luschny, "Divide, swing and conquer the factorial and the lcm{1,2,...,n}", preprint, April 2008.

LINKS

Peter Luschny, <a href="/A180000/a180000.pdf">Die schwingende Fakultät und Orbitalsysteme</a>, August 2011.

STATUS

approved

editing

#19 by Bruno Berselli at Thu Mar 02 02:33:01 EST 2017

STATUS

proposed

approved

#18 by Michel Marcus at Thu Mar 02 00:26:59 EST 2017

STATUS

editing

proposed

#17 by Michel Marcus at Thu Mar 02 00:26:50 EST 2017

COMMENTS

For n >= 0, k >= 0 let T(n,k) = sum{i=k..n} binomial(n-k,n-i)*(2i)$ where i$ denotes the swinging factorial of i (A056040). Triangle read by rows. For n >= 0, k >= 0 let

T(n,k) = sum{i=k..n} binomial(n-k,n-i)*(2i)$

where i$ denotes the swinging factorial of i (A056040).

STATUS

proposed

editing

#16 by Jon E. Schoenfield at Wed Mar 01 23:29:21 EST 2017

STATUS

editing

proposed

#15 by Jon E. Schoenfield at Wed Mar 01 23:29:14 EST 2017

EXAMPLE

Triangle begins

1;

3, 2;

11, 8, 6;

45, 34, 26, 20;

195, 150, 116, 90, 70;

873, 678, 528, 412, 322, 252;

3989, 3116, 2438, 1910, 1498, 1176, 924;

STATUS

proposed

editing

#14 by G. C. Greubel at Wed Mar 01 23:25:31 EST 2017

STATUS

editing

proposed

#13 by G. C. Greubel at Wed Mar 01 23:25:22 EST 2017

LINKS

G. C. Greubel, <a href="/A163841/b163841.txt">Table of n, a(n) for n = 0..1274the first 50 rows, flattened</a>

#12 by G. C. Greubel at Wed Mar 01 23:24:51 EST 2017

LINKS

G. C. Greubel, <a href="/A163841/b163841.txt">Table of n, a(n) for n = 0..1274</a>

STATUS

approved

editing