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Revision History for A129684

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A129684

Exponential Riordan array [1/(1-x^2/2), x].
(history; published version)

#7 by Peter Luschny at Fri Jul 19 14:26:39 EDT 2019

STATUS

proposed

approved

#6 by Michel Marcus at Fri Jul 19 13:16:11 EDT 2019

STATUS

editing

proposed

#5 by Michel Marcus at Fri Jul 19 13:16:06 EDT 2019

FORMULA

Number triangle T(n,k) = [k<=n](n!/k!)*(1/2^((n-k)/2))*(1+(-1)^(n-k))/2.

CROSSREFS

Cf. A087214, A129685.

STATUS

proposed

editing

#4 by Jean-François Alcover at Fri Jul 19 13:11:11 EDT 2019

STATUS

editing

proposed

#3 by Jean-François Alcover at Fri Jul 19 13:11:07 EDT 2019

MATHEMATICA

(* The function RiordanArray is defined in A256893. *)

RiordanArray[1/(1 - #^2/2)&, #&, 11, True] // Flatten (* Jean-François Alcover, Jul 19 2019 *)

STATUS

approved

editing

#2 by Russ Cox at Fri Mar 30 18:59:20 EDT 2012

AUTHOR

_Paul Barry (pbarry(AT)wit.ie), _, Apr 28 2007

Discussion

Fri Mar 30

18:59

OEIS Server: https://oeis.org/edit/global/287

#1 by N. J. A. Sloane at Fri May 11 03:00:00 EDT 2007

NAME

Exponential Riordan array [1/(1-x^2/2), x].

DATA

1, 0, 1, 1, 0, 1, 0, 3, 0, 1, 6, 0, 6, 0, 1, 0, 30, 0, 10, 0, 1, 90, 0, 90, 0, 15, 0, 1, 0, 630, 0, 210, 0, 21, 0, 1, 2520, 0, 2520, 0, 420, 0, 28, 0, 1, 0, 22680, 0, 7560, 0, 756, 0, 36, 0, 1, 113400, 0, 113400, 0, 18900, 0, 1260, 0, 45, 0, 1

OFFSET

0,8

COMMENTS

Row sums are A087214. Inverse is A129685.

FORMULA

Number triangle T(n,k)=[k<=n](n!/k!)*(1/2^((n-k)/2))*(1+(-1)^(n-k))/2

EXAMPLE

Triangle begins

1,

0, 1,

1, 0, 1,

0, 3, 0, 1,

6, 0, 6, 0, 1,

0, 30, 0, 10, 0, 1,

90, 0, 90, 0, 15, 0, 1,

0, 630, 0, 210, 0, 21, 0, 1

KEYWORD

easy,nonn,tabl,new

AUTHOR

Paul Barry (pbarry(AT)wit.ie), Apr 28 2007

STATUS

approved