A166335 Exponential Riordan array [1+x*sinh(x), x].

1, 0, 1, 2, 0, 1, 0, 6, 0, 1, 4, 0, 12, 0, 1, 0, 20, 0, 20, 0, 1, 6, 0, 60, 0, 30, 0, 1, 0, 42, 0, 140, 0, 42, 0, 1, 8, 0, 168, 0, 280, 0, 56, 0, 1, 0, 72, 0, 504, 0, 504, 0, 72, 0, 1, 10, 0, 360, 0, 1260, 0, 840, 0, 90, 0, 1

Offset: 0

Author

Paul Barry, Oct 12 2009

Keywords

• easy
• nonn
• tabl

Examples

			Triangle begins
1,
0, 1,
2, 0, 1,
0, 6, 0, 1,
4, 0, 12, 0, 1,
0, 20, 0, 20, 0, 1,
6, 0, 60, 0, 30, 0, 1,
0, 42, 0, 140, 0, 42, 0, 1,
8, 0, 168, 0, 280, 0, 56, 0, 1,
0, 72, 0, 504, 0, 504, 0, 72, 0, 1,
10, 0, 360, 0, 1260, 0, 840, 0, 90, 0, 1
		

Crossrefs

Row sums are A131056. Diagonal sums are A166336. Central coefficients are A166337.

Programs

Mathematica

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

Formula

Number triangle T(n,k)=[k<=n]*C(n,k)*((n-k)+0^((n-k)/2))(1+(-1)^(n-k))/2.