A159830 Exponential Riordan array [exp(exp(x)-1-2x),x].

1, -1, 1, 2, -2, 1, -3, 6, -3, 1, 7, -12, 12, -4, 1, -10, 35, -30, 20, -5, 1, 31, -60, 105, -60, 30, -6, 1, -21, 217, -210, 245, -105, 42, -7, 1, 204, -168, 868, -560, 490, -168, 56, -8, 1, 307, 1836, -756, 2604, -1260, 882, -252, 72, -9, 1, 2811, 3070, 9180, -2520, 6510, -2520, 1470, -360, 90, -10, 1

Offset: 0

Author

Paul Barry, Apr 23 2009

Keywords

• easy
• sign
• tabl

Comments

First column is A126617. Row sums are A000296. A007318*A159830 is A124323.

The inverse is [exp(-exp(x)+1+2x),x] which has production matrix given by

1, 1,

-1, 1, 1,

-1, -2, 1, 1,

-1, -3, -3, 1, 1,

-1, -4, -6, -4, 1, 1 ...

Examples

			Triangle begins
1,
-1, 1,
2, -2, 1,
-3, 6, -3, 1,
7, -12, 12, -4, 1,
-10, 35, -30, 20, -5, 1,
31, -60, 105, -60, 30, -6, 1,
-21, 217, -210, 245, -105, 42, -7, 1,
204, -168, 868, -560, 490, -168, 56, -8, 1
Production array is
-1, 1,
1, -1, 1,
1, 2, -1, 1,
1, 3, 3, -1, 1,
1, 4, 6, 4, -1, 1,
1, 5, 10, 10, 5, -1, 1,
1, 6, 15, 20, 15, 6, -1, 1,
1, 7, 21, 35, 35, 21, 7, -1, 1,
1, 8, 28, 56, 70, 56, 28, 8, -1, 1
		

Programs

Mathematica

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

Formula

G.f.: 1/(1-xy+x-x^2/(1-xy-2x^2/(1-xy-x-3x^2/(1-xy-2x-4x^2/(1-... (continued fraction).