The On-Line Encyclopedia of Integer Sequences (OEIS)

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A166378

Exponential Riordan array [1+x^2*sec(x), x].
(history; published version)

#5 by Alois P. Heinz at Fri Jul 19 14:25:54 EDT 2019

STATUS

proposed

approved

#4 by Jean-François Alcover at Fri Jul 19 13:35:16 EDT 2019

STATUS

editing

proposed

#3 by Jean-François Alcover at Fri Jul 19 13:35:13 EDT 2019

MATHEMATICA

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

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

STATUS

approved

editing

#2 by Russ Cox at Fri Mar 30 18:59:26 EDT 2012

AUTHOR

_Paul Barry (pbarry(AT)wit.ie), _, Oct 13 2009

Discussion

Fri Mar 30

18:59

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

#1 by N. J. A. Sloane at Tue Jun 01 03:00:00 EDT 2010

NAME

Exponential Riordan array [1+x^2*sec(x), x].

DATA

1, 0, 1, 2, 0, 1, 0, 6, 0, 1, 12, 0, 12, 0, 1, 0, 60, 0, 20, 0, 1, 150, 0, 180, 0, 30, 0, 1, 0, 1050, 0, 420, 0, 42, 0, 1, 3416, 0, 4200, 0, 840, 0, 56, 0, 1, 0, 30744, 0, 12600, 0, 1512, 0, 72, 0, 1, 124650, 0, 153720, 0, 31500, 0, 2520, 0, 90, 0, 1

OFFSET

0,4

COMMENTS

Row sums are A166379. Diagonal sums are A166380.

FORMULA

Number triangle T(n,k)=[k<=n]*A166377((n-k)/2)*C(n,k)*(1+(-1)^(n-k))/2.

EXAMPLE

Triangle begins

1,

0, 1,

2, 0, 1,

0, 6, 0, 1,

12, 0, 12, 0, 1,

0, 60, 0, 20, 0, 1,

150, 0, 180, 0, 30, 0, 1,

0, 1050, 0, 420, 0, 42, 0, 1,

3416, 0, 4200, 0, 840, 0, 56, 0, 1,

0, 30744, 0, 12600, 0, 1512, 0, 72, 0, 1,

124650, 0, 153720, 0, 31500, 0, 2520, 0, 90, 0, 1

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry (pbarry(AT)wit.ie), Oct 13 2009

STATUS

approved