The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A000255 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A000255

a(n) = n*a(n-1) + (n-1)*a(n-2), a(0) = 1, a(1) = 1.
(history; published version)

#315 by N. J. A. Sloane at Sat Nov 02 00:04:40 EDT 2024

STATUS

proposed

approved

#314 by Shenghui Yang at Wed Oct 16 00:45:22 EDT 2024

STATUS

editing

proposed

Discussion

Wed Oct 16

00:45

Shenghui Yang: Implementation based on this entry: "Also, for n > 0, determinant of the tridiagonal n X n matrix M such that M(i,i)=i and for i=1..n-1, M(i,i+1)=-1, M(i+1,i)=i. - Mario Catalani (mario.catalani(AT)unito.it), Feb 04 2003"

Fri Nov 01

17:03

Sean A. Irvine: Any reason not to use "a[k]" rather than "sa[k]"?

19:15

Shenghui Yang: "sa" emphasizes that this implemation uses sparse array.

19:18

Shenghui Yang: Therefore `MatrixForm[sa[10]]` should work and this OEIS sequence is obtained by a[10] = Det[sa[10]]

#313 by Shenghui Yang at Wed Oct 16 00:45:14 EDT 2024

MATHEMATICA

sa[k_Integer]/; k>=2 := SparseArray[{{i_, i_} -> i, Band[{2, 1}] -> -1, {i_, j_} /; (i == j - 1) :> i}, {k, k}]; {1, 1}~Join~Array[Det[sa[#]] &, 20, 2] (* Shenghui Yang, Oct 15, 2024 *)

STATUS

approved

editing

#312 by Peter Luschny at Wed Jul 17 16:56:51 EDT 2024

STATUS

proposed

approved

#311 by Michael De Vlieger at Wed Jul 17 16:55:24 EDT 2024

STATUS

editing

proposed

#310 by Michael De Vlieger at Wed Jul 17 16:55:20 EDT 2024

LINKS

Hannah Golab, <a href="http://danaernst.com/scholarship/GolabThesis.pdf">Pattern avoidance in Cayley permutations</a>, Master's Thesis, Northern Arizona Univ. (2024). See p. 36.

STATUS

approved

editing

#309 by Michael De Vlieger at Mon Apr 15 12:59:53 EDT 2024

STATUS

reviewed

approved

#308 by Michel Marcus at Mon Apr 15 12:56:19 EDT 2024

STATUS

proposed

reviewed

#307 by Michael De Vlieger at Mon Apr 15 12:42:52 EDT 2024

STATUS

editing

proposed

#306 by Michael De Vlieger at Mon Apr 15 12:42:47 EDT 2024

LINKS

Jun Yan, <a href="https://arxiv.org/abs/2404.07958">Results on pattern avoidance in parking functions</a>, arXiv:2404.07958 [math.CO], 2024. See p. 5.

STATUS

approved

editing