A166378 Exponential Riordan array [1+x^2*sec(x), x].

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.

Links

Table of n, a(n) for n=0..65.

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

Mathematica

(* The function RiordanArray is defined in A256893. *)
RiordanArray[1 + #^2 Sec[#]&, #&, 11, True] // Flatten (* Jean-François Alcover, Jul 19 2019 *)

Crossrefs

Sequence in context: A166357 A067147 A112227 * A249820 A136579 A249731

Adjacent sequences: A166375 A166376 A166377 * A166379 A166380 A166381

Keyword

easy,nonn,tabl

Author

Paul Barry, Oct 13 2009

Status

approved