The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A084938 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A084938

Triangle read by rows: T(n,k) = Sum_{j>=0} j!*T(n-j-1, k-1) for n >= 0, k >= 0.
(history; published version)

#138 by Andrey Zabolotskiy at Thu Jan 18 05:57:18 EST 2024

STATUS

reviewed

approved

#137 by Michel Marcus at Thu Jan 18 05:24:03 EST 2024

STATUS

proposed

reviewed

#136 by Joerg Arndt at Thu Jan 18 04:59:15 EST 2024

STATUS

editing

proposed

#135 by Joerg Arndt at Thu Jan 18 04:57:56 EST 2024

CROSSREFS

Cf. A134378, A134379, A165489, A165490, A287899.

Cf. A287899.

Discussion

Thu Jan 18

04:59

Joerg Arndt: removed advertisements for unimportant sequences

#134 by Joerg Arndt at Thu Jan 18 04:57:13 EST 2024

COMMENTS

Eigensequence of the triangle = A165489: (1, 1, 2, 6, 23, 105, 550, 3236, ...). - Gary W. Adamson, Sep 20 2009

#133 by Joerg Arndt at Thu Jan 18 04:56:14 EST 2024

COMMENTS

This triangle * [1,2,3,...] = A134378: (1, 2, 5, 14, 44, 158, 663, ...) = row sums of triangle A134379. - Gary W. Adamson, Oct 22 2007

STATUS

approved

editing

#132 by Andrey Zabolotskiy at Fri Dec 29 22:23:06 EST 2023

STATUS

editing

approved

#131 by Andrey Zabolotskiy at Fri Dec 29 22:22:56 EST 2023

COMMENTS

In general, the triangle [r_0,r_1,r_2,r_3,...] DELTA [s_0,s_1,s_2,s_3,...] has generating function 1/(1-(r_0*x+s_0*x*y)/(1-(r_1*x+s_1*x*y)/(1-(r_2*x+s_2*x*y)/(1-(r_3*x+s_3*x*y)/(1-...(continued fraction). See also the Formula section below.

STATUS

approved

editing

#130 by Amiram Eldar at Fri Jul 14 04:15:14 EDT 2023

STATUS

editing

approved

#129 by Amiram Eldar at Fri Jul 14 04:15:11 EDT 2023

LINKS

Paul Barry, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL12/Barry3/barry93.html">Continued fractions and transformations of integer sequences</a>, JIS 12 (2009) , Article 09.7.6.

Paul Barry and A. Hennessy, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL14/Barry2/barry126.html">A Note on Narayana Triangles and Related Polynomials, Riordan Arrays, and MIMO Capacity Calculations</a>, J. Int. Seq. 14 (2011) # , Article 11.3.8.

STATUS

reviewed

editing