The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A008282 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A008282

Triangle of Euler-Bernoulli or Entringer numbers read by rows: T(n,k) is the number of down-up permutations of n+1 starting with k+1.
(history; published version)

#93 by Alois P. Heinz at Sat Aug 03 16:44:37 EDT 2024

STATUS

proposed

approved

#92 by Jason Yuen at Sat Aug 03 16:29:21 EDT 2024

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editing

proposed

#91 by Jason Yuen at Sat Aug 03 16:29:15 EDT 2024

FORMULA

Sum_{n=0..oo} Sum_{k=0..n} T(n,k) x^(n-k})/(n-k)! * y^k/k! = {cos x + sin y}/cos(x + y).

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approved

editing

#90 by N. J. A. Sloane at Sun Feb 06 12:42:10 EST 2022

STATUS

editing

approved

#89 by N. J. A. Sloane at Sun Feb 06 12:42:07 EST 2022

FORMULA

Sum_{n=0..oo} Sum_{k=0..n} T(n,k) x^{(n-k}}/(n-k)! * y^k/k! = {cos x + sin y}/cos(x + y).

STATUS

approved

editing

#88 by N. J. A. Sloane at Sun Feb 06 12:40:35 EST 2022

STATUS

editing

approved

#87 by N. J. A. Sloane at Sun Feb 06 12:40:19 EST 2022

FORMULA

Comment from Masanobu Kaneko: (Start)

A generating function that applies for all n, both even and odd:

Sum_{n=0..oo} Sum_{k=0..n} T(n,k) x^{n-k}}/(n-k)! * y^k/k! = {cos x+sin y}/cos(x+y).

(End) - N. J. A. Sloane, Feb 06 2022

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approved

editing

#86 by Michel Marcus at Wed Feb 17 09:23:30 EST 2021

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reviewed

approved

#85 by Joerg Arndt at Wed Feb 17 08:04:09 EST 2021

STATUS

proposed

reviewed

#84 by Petros Hadjicostas at Wed Feb 17 07:57:44 EST 2021

STATUS

editing

proposed